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Related Questions
What is the meaning of "If dom(f) = [tex]X^{n}[/tex], then f is an n-ary function on X"?
Answers
The statement "If dom(f) = Χ, then f is an n-ary functionon X" means that if the domain of the function f is equal to the set X, then f is considered an n-ary function on X.
How is this so?In other words, for each element in X, the function f can take n arguments or inputs to produce aunique output. The term "n-ary" indicates the number of arguments that the function can accept.
A statement in mathematics is a declarative utterance that is either true or untrue but not both. A proposal is anothername for a statement. The main point is that there should be no uncertainty.
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Answer:
The statement "If dom(f) = X, then f is an n-ary function on X" means that if the domain of a function f is equal to the set X, then f is a function that takes n arguments or inputs from the set X, where the value of n depends on the specific function.
Step-by-step explanation:
The statement "If dom(f) = X", then f is an n-ary function on X" means that if the domain of the function f is equal to the set X, then f is an n-ary function on X.
Here's a breakdown of the terms used in the statement:
- dom(f): The domain of a function f refers to the set of all possible input values for the function. It represents the set of values for which the function is defined.
- X: In this context, X represents a set. It could be any set, and it serves as the domain for the function f.
- n-ary function: An n-ary function is a function that takes n arguments or inputs. The value of n represents the number of inputs the function expects.
Therefore, the statement is saying that if the domain of the function f is equal to the set X, then f is an n-ary function on X. It implies that the function f takes n inputs from the set X, where n is determined by the specific function.
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solve each equation 1/3a= -15
Answers
The solution to the equation 1/3a = -15 is a = -45
How to determine the solution to the equationfrom the question, we have the following parameters that can be used in our computation:
1/3a = -15
Multiply 3 to both sides of the equation
so, we have the following representation
3 * 1/3a = -15 * 3
When the products are evalated, we have
a = -45
Hence, the solution to the equation is a = -45
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Please I need solution and steps
Answers
Answer:
Refer to the step-by-step, follow along carefully.
Step-by-step explanation:
Verify the given identity.
[tex]\frac{\sin(x)}{1-\cos(x)} -\frac{\sin(x)\cos(x)}{1+\cos(x)} =\csc(x)(1+\cos^2(x))[/tex]
Pick the more complicated side to manipulate, so the L.H.S.
(1) - Combine the fractions with a common denominator
[tex]\frac{\sin(x)}{1-\cos(x)} -\frac{\sin(x)\cos(x)}{1+\cos(x)}\\\\\Longrightarrow \frac{\sin(x)(1+\cos(x))}{(1-\cos(x))(1+\cos(x))} -\frac{\sin(x)\cos(x)(1-\cos(x))}{(1+\cos(x))(1-\cos(x))} \\\\\Longrightarrow \frac{\sin(x)+\sin(x)\cos(x)-\sin(x)\cos(x)+\sin(x)\cos^2(x)}{(1+\cos(x))(1-\cos(x))} \\\\\Longrightarrow \boxed{\frac{\sin(x)+\sin(x)\cos^2(x)}{(1+\cos(x))(1-\cos(x))}} \\\\[/tex]
(2) - Simplify the denominator
[tex]\frac{\sin(x)+\sin(x)\cos^2(x)}{(1+\cos(x))(1-\cos(x))}\\\\\Longrightarrow \frac{\sin(x)+\sin(x)\cos^2(x)}{1-\cos(x)+\cos(x)-\cos^2(x)}\\\\\Longrightarrow \boxed{\frac{\sin(x)+\sin(x)\cos^2(x)}{1-\cos^2(x)}}[/tex]
(3) - Apply the following Pythagorean identity to the denominator
[tex]\boxed{\left\begin{array}{ccc}\text{\underline{Pythagorean Identity:}}\\\\1-\cos^2(\theta)=\sin^2(\theta)\end{array}\right}[/tex]
[tex]\frac{\sin(x)+\sin(x)\cos^2(x)}{1-\cos^2(x)}\\\\\Longrightarrow \boxed{\frac{\sin(x)+\sin(x)\cos^2(x)}{\sin^2(x)}}[/tex]
(4) - Simplify the fraction and split it up
[tex]\frac{\sin(x)+\sin(x)\cos^2(x)}{\sin^2(x)}\\\\\Longrightarrow \frac{1+\cos^2(x)}{\sin(x)}\\\\\Longrightarrow \boxed{\frac{1}{\sin(x)}+\frac{\cos^2(x)}{\sin(x)}}[/tex]
(5) - Apply the following reciprocal identity
[tex]\boxed{\left\begin{array}{ccc}\text{\underline{Reciprocal Identitiy:}}\\\\\csc(\theta)=\frac{1}{\sin(\theta)} \end{array}\right}[/tex]
[tex]\frac{1}{\sin(x)}+\frac{\cos^2(x)}{\sin(x)}\\\\\Longrightarrow \csc(x)+\frac{1}{\sin(x)}\cos^2(x) \\\\\Longrightarrow \csc(x)+\csc(x)\cos^2(x) \\\\\therefore \boxed{\boxed{\csc(x)(1+\cos^2(x))}}[/tex]
Thus, the identity is verified.
Prove of the expression sin x / (1 - cos x) - [sin x cos x ] / (1 + cos x) by using trigonometry formula is shown below.
We have to given that,
Expression to verify is,
⇒ sin x / (1 - cos x) - [sin x cos x ] / (1 + cos x)
Now, We can simplify as,
⇒ sin x / (1 - cos x) - [sin x cos x ] / (1 + cos x)
⇒ sin x [ 1 / (1 - cos x) - cos x / (1 + cos x)]
⇒ sin x [1 + cos x - cos x (1 - cos x )] / (1 - cos²x)
⇒ sin x [1 + cos x - cos x + cos²x] / sin²x
⇒ (1 + cos²x) / sin x
⇒ cosec x (1 + cos²x)
Thus, Prove of the expression sin x / (1 - cos x) - [sin x cos x ] / (1 + cos x) by using trigonometry formula is shown above.
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Picture included!!! Please help! Suppose a = 10 and b = 24. Give the value of each of the following. Give answers as integers or rounded to 2 decimal places as appropriate.
Answers
Answer:
A = 22.62°
B = 67.38°
c = 26
Step-by-step explanation:
[tex]a^2+b^2=c^2\\10^2+24^2=c^2\\100+576=c^2\\676=c^2\\26=c[/tex]
[tex]\sin A=\frac{\text{Opposite}}{\text{Hypotenuse}}=\frac{10}{26}\\\\A=\sin^{-1}(\frac{10}{26})\\\\A\approx22.62^\circ[/tex]<-- You can also use other trig ratios
[tex]B=180^\circ-(90^\circ+22.62^\circ)=180^\circ-112.62^\circ=67.38^\circ[/tex]
There's no specific order in how to solve for A and B, so there may be more than one way to approach these solutions.
100 Points! Geometry question. Photo attached. Please show as much work as possible. Thank you!
Answers
Next, we add the two bases to get 21: 6+15=21 (h=2 x 136.5)
Then, divide the total of the two bases (21) from the area to get 6.5: 136.5/21-6.5
Finally we multiply 2 by 6.5: 2 x 6.5= 13
The height if this trapezoid is 13.
Answer:
13cm
Step-by-step explanation:
The area of a trapezoid is given by the formula:
Area = ½*(b1+b2)*h
where:
b1 and b2 are the lengths of the bases of the trapezoid h is the height of the trapezoidIn this problem, we are given that b1 = 6 cm, b2 = 15 cm, and Area = 136.5 square centimeters.
Plugging these values into the formula, we get:
136.5 = ½*(6 + 15)*h
Solving for h, we get:
136.5=10.5h
h = 136.5/10.5=13centimeters
Therefore, the height of the trapezoid is 13 centimeters.
Complete the proof that HJ LGI.
4
I
5
Statement
K
1
ZHKI ZGKH
2
m2GKH + mZHKI = 180°
3 m2GKH+mZGKH= 180°
mZGKH = 90°
HJ L GI
G
H
Reason
Given
Angles forming a linear pair sum to 180°
Definition of congruence
(
Answers
The complete sentence is shown below:
Reason: Given
Reason: Angles forming a linear pair sum to 180° (Given)
Reason: Substitution from Statement 1.
To complete the proof that HJ GI, we can use the given statements and reasons:
Statement 1: <HKI = <GKH
Reason: Given
Statement 2: m<GKH + m<HKI = 180°
Reason: Angles forming a linear pair sum to 180° (Given)
Statement 3: m,GKH + m<GKH = 180°
Reason: Substitution from Statement 1
Statement 4: m<GKH = 90°
Reason: From Statement 2 and Statement 3, we can subtract m<GKH from both sides, which results in m<GKH = 180° - m<GKH.
Since the angles forming a linear pair sum to 180°, m<GKH + m<GKH = 180° implies that m<GKH = 90°.
Therefore, based on the given statements and reasons, we can conclude that HJ and GI are congruent (m<GKH = 90°)
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2x + y ≤ 2
a. change the inequality into slope-intercept form, and then change it into an equation.
b. create a table. Use the x-values indicated
c. Graph the points and draw a line.
d. Shade the solution area.
e. Check your solution. Use (0,0) as your test point and see if it satisfies the conditions of the original inequality.
Answers
2x + y ≤ 2
y ≤ -2x + 2
To change it into an equation, we remove the inequality symbol and obtain:
y = -2x + 2
b. Using the x-values indicated, we can create a table of corresponding y-values:
|x | y |
|---|---|
|0 | 2 |
|1 | 0 |
|2 |-2 |
c. To graph the points and draw a line, we plot the points (0, 2), (1, 0), and (2, -2) on the coordinate plane and connect them with a straight line.
d. To shade the solution area, we need to determine which side of the line satisfies the inequality. Since the inequality is less than or equal to, we shade the area below the line.
e. To check the solution, we plug in the test point (0, 0) into the original inequality:
2x + y ≤ 2
2(0) + 0 ≤ 2
0 ≤ 2
The inequality holds, so the point (0, 0) is in the shaded area and satisfies the conditions of the original inequality. Therefore, the solution is valid.
Find the surface area
of the figure below:
19 cm
30 cm.
Answers
The surface area of the figure is approximately 997.5π cm².
We have,
The figure has two shapes:
Cone and a semicircle
Now,
The surface area of a cone:
= πr (r + l)
where r is the radius of the base and l is the slant height.
Given that
r = 15 cm and l = 19 cm, we can substitute these values into the formula:
= π(15)(15 + 19) = 885π cm² (rounded to the nearest whole number)
The surface area of a semicircle:
= (πr²) / 2
Given that r = 15 cm, we can substitute this value into the formula:
= (π(15)²) / 2
= 112.5π cm² (rounded to one decimal place)
The surface area of the figure:
To find the total surface area of the figure, we add the surface area of the cone and the surface area of the semicircle:
Now,
Total surface area
= 885π + 112.5π
= 997.5π cm² (rounded to one decimal place)
Therefore,
The surface area of the figure is approximately 997.5π cm².
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For what value of x is the rational expression below undefined?
x-3
3+x
A. 3
OB. -1
O C. 0
OD. -3
Answers
The value of x that makes the rational expression undefined is x = -3.
The rational expression is undefined when the denominator is equal to zero, because division by zero is undefined.
In the given rational expression (x - 3) / (3 + x), we need to find the value of x that makes the denominator (3 + x) equal to zero.
To find this value, we set the denominator equal to zero and solve for x:
3 + x = 0
Subtracting 3 from both sides:
x = -3
Therefore, the value of x that makes the rational expression undefined is x = -3.
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Find x to the nearest hundredth.
16
X
40°
OA. x = 24.89
OB. x = 13.43
O C. x 10.28
OD. x = 12.26
Answers
Sin 40° = x/16
0.6428 = x/16
x = 0.643 × 16
x = 10.2848
x = 10.28
So, the value of x is 10.28 (C)
That's it :)
If (2x-7), (x-1), 3x, x, (x+2), 30 and 10
1. Find the value of x
2. Find the value of the largest angle
PLEASE HELP ME ASAP
Answers
The value of x in arithmetic progression is 5/3 and the largest angle is 30.
The given sequence is: (2x-7), (x-1), 3x, x, (x+2), 30, 10.
In an arithmetic progression, the common difference (d) between consecutive terms remains constant.
The common difference between the terms = (x - 1) - (2x - 7) = x - 1 - 2x + 7 = 6 - x
6 - x = 3x - (x - 1)
6 - x = 3x - x + 1
6 - x = 2x + 1
-x - 2x = 1 - 6
-3x = -5
x = -5 / -3
x = 5/3
Therefore, the value of x is 5/3.
2x-7 = 2 ×5/3 -7 = -3.66
x-1 = 5/3-7 = -5.33
3x = 3 × 5/3 = 5
x + 2 = 5/3+2 =3.66
Thus, the largest angle is 30.
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Your question is incomplete, most probably the full answer is:
If (2x-7), (x-1), 3x, x, (x+2), 30 and 10 are in AP, then
1. Find the value of x
2. Find the value of the largest angle
In the given circle the m∠J
is 88°, mArc DF is 62° and mArc BD is 136° what is the m∠
C ?
Answers
The measure of angle C is 13°.
To find the measure of angle C in the given circle, we need to use the properties of angles subtended by arcs in a circle.
Given information:
m∠J = 88° (angle J)
mArc DF = 62° (arc DF)
mArc BD = 136° (arc BD)
We can start by using the fact that the measure of an angle formed by a chord and an arc is equal to half the measure of the intercepted arc.
Since mArc DF = 62°, the measure of angle DJF (angle formed by chord DF and arc DF) is 62°/2 = 31°.
Next, we can use the fact that angles subtended by the same arc are equal.
Since mArc BD = 136°, angle BJD (angle formed by chord BD and arc BD) is also 136°.
Now, let's find angle BCD (angle formed by chord BD and chord CD). The sum of angles in a triangle is 180°, so angle BCD = 180° - angle DJF - angle BJD.
Angle BCD = 180° - 31° - 136°
Angle BCD = 180° - 167°
Angle BCD = 13°
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Tariq has $640 to spend at a bicycle store for some new gear and biking outfits. Assume all prices listed include tax.
He buys a new bicycle for $291.24.
He buys 4 bicycle reflectors for $19.56 each and a pair of bike gloves for $16.52.
He plans to spend some or all of the money he has left to buy new biking outfits for $50.80 each.
Write and solve an inequality which can be used to determine
x, the number of outfits Tariq can purchase while staying within his budget.
Answers
Let's solve the inequality to determine the number of outfits Tariq can purchase while staying within his budget.
Given:
Amount Tariq has to spend: $640
Cost of a new bicycle: $291.24
Cost of 4 bicycle reflectors: $19.56 each
Cost of bike gloves: $16.52
Cost of each biking outfit: $50.80
Let's assume the number of outfits Tariq can purchase is represented by x.
The total cost of the items he has already purchased is:
Cost of bicycle = $291.24
Cost of 4 bicycle reflectors = $19.56 * 4 = $78.24
Cost of bike gloves = $16.52
The remaining amount Tariq has to spend can be calculated as:
Remaining amount = Total amount - (Cost of bicycle + Cost of reflectors + Cost of gloves)
Remaining amount = $640 - ($291.24 + $78.24 + $16.52)
Now, we need to determine the maximum number of outfits Tariq can purchase with the remaining amount. Each outfit costs $50.80.
Inequality: x * $50.80 ≤ Remaining amount
Substituting the values:
x * $50.80 ≤ $640 - ($291.24 + $78.24 + $16.52)
Simplifying further:
x * $50.80 ≤ $640 - $385
x * $50.80 ≤ $255
To solve for x, we divide both sides of the inequality by $50.80:
x ≤ $255 / $50.80
x ≤ 5
Therefore, the maximum number of outfits Tariq can purchase while staying within his budget is 5.
Factor the following and then fill in the blanks. 2x²7x-15 = (2x + )(x- Blank 1: Blank 2:
Answers
Answer:
(2x + 3)(x - 5)
Step-by-step explanation:
2x² - 7x - 15
consider the factors of the product of the coefficient of the x² term and the constant term which sum to give the coefficient of the x- term
product = 2 × - 15 = - 30 and sum = - 7
the factors are - 10 and + 3
use these factors to split the x- term
2x² - 10x + 3x - 15 ( factor the first/second and third/fourth terms )
= 2x(x - 5) + 3(x - 5) ← factor out (x - 5) from each term
= (2x + 3)(x - 5) ← in factored form
Blank 1 is 3
Blank 2 is 5
50 Points! Multiple choice geometry question. Photo attached. Thank you!
Answers
area of equilateral triangle =
[tex]( \sqrt{3 } \div 4) \times a {}^{2} [/tex]
(C) area = 84.9 in²
What is the 10th term of the geometric sequence where a1 = 384 and a7 = 6?
0.75
3
6
1.5
Answers
Answer:
(a) 0.75
Step-by-step explanation:
You want the 10th term of the geometric sequence with a1 = 384 and a7 = 6.
N-th termThe equation for the n-th term can be written ...
an = a1·b^(n-1)
Using a1 = 384, we can find b from ...
a7 = 6 = 384·b^(7-1)
(6/384)^(1/6) = b
10th termThen the 10th term is ...
a10 = 384·(6/384)^((10-1)/6) = 0.75
The 10th term of the sequence is 0.75.
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The aquarium has 10 more red fish than blue fish. 60 percent of the fish are red. How many blue fish are in the aquarium? Show your work. (10 points)
Answers
Answer:
There are 20 blue fish in the aquarium.
Step-by-step explanation:
If 60% of the fish are red than 40% are blue. That means that 20% fish is 10 fish. 20% = 10 fish. 40% = 20 fish.
find the center of the circle that you can circumscribe about triangle ABC. A(2,8) B(0,8) C(2,2)
Answers
The center of the circumscribed circle is (1, 5).
How do we calculate?We calculate the midpoint and slope of the line segment AB:
Midpoint of AB = ((x₁ + x₂) / 2, (y₁ + y₂) / 2)
Midpoint of AB = ((2 + 0) / 2, (8 + 8) / 2)
Midpoint of AB = (1, 8)
Slope of AB = (y₂ - y₁) / (x₂ - x₁)
= (8 - 8) / (0 - 2)
Slope= 0
We can notice that the equation of the perpendicular bisector of AB is x = 1.
We also find midpoint and slope of the line segment BC
Midpoint of BC = ((x₁ + x₂) / 2, (y₁ + y₂) / 2)
= ((0 + 2) / 2, (8 + 2) / 2)
= (1, 5)
Slope of BC = (y₂ - y₁) / (x₂ - x₁)
= (2 - 8) / (2 - 0)
= -3
y - 5 = -3(x - 1)
y - 5 = -3x + 3
3x + y = 8
we have the equations of two perpendicular bisectors which are
x = 1 and 3x + y = 8.
We Substitute x = 1 into 3x + y = 8:
3(1) + y = 8
3 + y = 8
y = 5
In conclusion, center of the circumscribed circle is (1, 5).
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WILL GIVE BRAINLIEST FOR THE CORRECT ANSWER!!
What scale factor was applied to the first rectangle to get the resulting image?
Enter your answer as a decimal in the box.
Answers
Answer:
2.5
Step-by-step explanation:
the length has increased by 7.5/3 = 2.5.
so the scale factor is 2.5
30 POINTS!! PLEASE
A surveyor wants to determine the width of a river. She surveys the area and finds the following measures below.
She uses a pair of similar triangles, to help her find the answer.
Answers
Answer:
D = 90 FT
Step-by-step explanation:
40 / d = 20 / 45
cross multiply
45 × 40 = 20d
1800 = 20d
divide both sides by 20
1800 / 20 = 20d / 20
d = 90 ft
Please help ASAP 7p-13p+4-5p
Answers
Hello!
[tex]7p-13p+4-5p\\\\= 7p-13p-5p+4\\\\= -6p-5p+4\\\\\Large\boxed{= -11p + 4}[/tex]
50 Points! Multiple choice geometry question. Photo attached. Thank you!
Answers
The angle ABC in the circle is 70 degrees.
How to find the angle in a circle?The intercepted arc is the arc that is inside the inscribed angle and whose
endpoints are on the angle. The arc angle is half the the inscribed angle.
The intercepted arc that is formed is equal to the inscribed angle,
multiplied by two (intercepted arc measure = inscribed angle × 2).
Therefore, let's find the arc angle ABC as follows:
∠ ABC = 1 /2 (360 - 120 - 100)
∠ ABC = 1 /2 (360 - 220)
∠ ABC = 1 /2 (140)
Therefore,
∠ ABC = 70 degrees
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Help me a123 sq ft
B61 sq ft
C49sq ft
D110 sq ft
Answers
The area of the required shaded portion is 123 ft²
Given is figure having some shaded portion we need to find the area of the same,
So, the shaded portion is two right isosceles triangles with equal side measuring 14 ft and 7 ft,
So, to find the same, we will calculate the area of the triangles and add them,
Area of a triangle = 1/2 x base x height
Area of the shaded portion = 1/2 x 7 x 7 + 1/2 x 14 x 14
= 122.5 ft²
≈ 123 ft²
Hence the area of the required shaded portion is 123 ft²
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Find the missing dimension of the cylinder. Round your answer to the nearest whole number.
Volume = $\ 10,000\pi\ $ in.3
A cylindrical piece of a log is shown. The diameter of its base is 32 inches and height is h.
$h\ \approx$
in.
Answers
The nearest Whole number, the missing dimension (height) of the cylinder is approximately 39 inches.
The missing dimension of the cylinder, we can use the formula for the volume of a cylinder:
Volume = π * r^2 * h
Given that the volume is 10,000π in³ and the diameter of the base is 32 inches, we can determine the radius (r) of the cylinder.
The diameter is twice the radius, so the radius is half of the diameter:
r = 32 inches / 2 = 16 inches
Substituting the known values into the volume formula, we have:
10,000π in³ = π * (16 in)^2 * h
Cancelling out the common factor of π, we get:
10,000 = 16^2 * h
Simplifying further:
10,000 = 256 * h
To isolate h, we divide both sides of the equation by 256:
h = 10,000 / 256
Calculating the value of h:
h ≈ 39.06
Rounded to the nearest whole number, the missing dimension (height) of the cylinder is approximately 39 inches.
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What is 4∑5n=1 equal to? (See picture below)
Did I get it right?
Answers
The summation of 5 to power of n (where n starts from 1) is determined as 625.
What is the sum of the number?The sum of the expression given is calculated by using the defined expression as sated in the question to perform the summation.
The given summation expression include;
∑5ⁿ
where;
n is defined to start from 1. (this written as n = 1)So we are going to sum the number 5ⁿ 4 times.
The expression becomes;
5ⁿ x 5ⁿ x 5ⁿ x 5ⁿ = 5⁴ⁿ
where;
n = 1
The summation becomes;
5⁴ⁿ = 5⁴ = 625
Thus, the summation of 5 to power of n (where n starts from 1) is determined as 625.
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The consistency of the diameters of wheel bearings is vital to the operation of the wheel. The specifications require that the variance of these diameters be no more than 0.0015 centimeter squared. The diameter is continually monitored by the quality-control team. Twenty subsamples of size 10 are obtained every day. One of these subsamples produced bearings that had a variance of 0.00317 centimeter squared. Conduct a hypothesis test to determine if the quality control team should advise management to stop production and search for causes of the inconsistency of the bearing diameters. Use a significance level of 0.05.
Answers
In the year 2000, population
Answers
In the year 2000, it was estimate that the population of the world was 6, 082, 966, 429 people.
What was the world population in 2000 ?Based on data provided by the table give, the global population in the year 2000 was estimated to be around 6, 082, 966, 429 individuals. This remarkable figure, serving as a testament to the expansive tapestry of humanity, reflects the vastness and intricacy of our interconnected world during that period.
Within the context of demographic analysis, the United Nations diligently compiled and analyzed extensive data to derive this population estimate for statistical reasons.
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The full question is:
In the year 2000 the world population was
If 2 pints = 1 quart and 1 quart = 1 pint then how many pints are 2 quarts?
Answers
Step-by-step explanation:
1 qt = 2 pts multiply both sides by two
2 qt = 4 pints
25. Three students contributed a total of $200 towards a building for the aged. Azar contributed 50% of it, Sunil 25% and the rest was contributed by a girl Becky. How much money did Becky contribute? rice he lost 25% of its weight
Answers
Becky contributed $50 towards the building for the aged.
Let's calculate the amounts contributed by each student:
Azar contributed 50% of the total amount:
Amount contributed by Azar = 50% of $200
= (50/100) × $200
= $100
Sunil contributed 25% of the total amount:
Amount contributed by Sunil = 25% of $200
= (25/100) × $200
= $50
Now, we can calculate the amount contributed by Becky:
Total contribution by Azar and Sunil = $100 + $50 = $150
The remaining amount contributed by Becky can be found by subtracting the total contribution by Azar and Sunil from the total amount:
Amount contributed by Becky = Total amount - Total contribution by Azar and Sunil
= $200 - $150
= $50
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#8: Expand the logarithm shown below. *
log981xy
Answers
In order to expand the properties of logarithms log981x:
log981x = log98 + log1x
One must know that loga + logb = log(ab), and loga + logb = log(ab) may also be represented as loga(b) or logab.
Using this property, we can simplify the expression further:
log981x = log98 + log1x = log9 + log8 + log1 + logx
We know that log9 = 2 and log1 = 0, so we can simplify even further:
log981x = log9 + log8 + log1 + logx = 2 + log8 + 0 + logx = 2 + log8x.
Therefore, the expanded value would be log981x to 2 + log8x.
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