Sam is proving the product property of logarithms. Step justification given substitution which expression and justification completes the third step of her proof? ; power rule of exponents subtraction property of exponents multiplication rule of exponents division property of exponents.

Answers

Answer 1

Sam's rationale for the third step based on logarithm properties would be logb(b^x+y), power rule of exponents. Thus, the correct answer is C.

The first step of Sam's proof is to show that logb(MN) is equal to logb(b^x.b^y), which is a substitution of MN for b^x.b^y. This is based on the product property of logarithms, which states that logb(MN) = logb(M) + logb(N) for any positive numbers M and N and any base b, as long as b doesn't equal 1.

The third step of her proof is to simplify logb(b^x.b^y) further by applying the power rule of exponents, which states that:

b^(x+y) = b^x.b^y

So, by substituting b^(x+y) for b^x.b^y, we get:

logb(b^(x+y)) = logb(b^x+y)

So, in short, the justification of the third step is based on the power rule of exponents, and it shows that logb(b^x.b^y) can be simplified further to logb(b^x+y).

The answer choice A, logb(b^xy), power rule of exponents, is incorrect because it implies that the third step is to multiply x and y instead of adding them.

This question should be provided with answer choices, which are:

A. logb(b^xy), power rule of exponents.B. logb(b^x-y), subtraction property of exponents.C. logb(b^x+y), power rule of exponents.D. logb(b^x/y), division property of exponents.

The correct answer is C.

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Sam Is Proving The Product Property Of Logarithms. Step Justification Given Substitution Which Expression
Answer 2

Answer: its c

Step-by-step explanation:

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Related Questions

Damian’s computer repair shop earned $2,500 in income last week. Expenses were $2,750. What was Damian’s profit or loss for the week?

Answers

Answer:

2500-2750 = - 250

hence,he lost $250

Help me plz i will give brainlest

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Answer:

the answer should be (3,-2)

answer quickly and quietly incorrectly please

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Answer:

Your answer is

A & E

Mark my answer as brainlist . I need that urgently . Folow me for more answer.

Step-by-step explanation:

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Answers

Answer: a: 23.4

Step-by-step explanation:

Answer:

A.23.4

Step-by-step explanation:

first find the volume of the tank 18x12x25=5400 then find how many gallons of water tank can hold 5400/231=23.4

hope this helps have a blessed day :)

HELPPPPPPP pleaseeeee mathhhh

Answers

9514 1404 393

Answer:

  y = 1/6x

Step-by-step explanation:

The constant of proportionality is the ratio of y to x:

  k = y/x

Using the point you have circled, it is ...

  k = 2/12 = 1/6

Then the equation y = kx can be written:

  y = 1/6x

Which expression is equivalent to 1/4(12x + 16) + 3x + 7

Please help!!!

a. 15/4x + 7
b. 15x + 23
c. 6x + 23
d. 6x + 11

Answers

Answer:

the answer is 6x+11

Step-by-step explanation:

1/4(12+16)+3x+7

1/4×4(3x+4)+3x+7

(3x+4)+3x+7

3x+4+3x+7

6x+11

The translation shown in the graph moves the figure to the right. What kind of translation is shown?

Answers

the figure go to the left

If
f(x) = x^2 + 2x - 4
and
g(x) = 3x + 1
Find
f(g(x)) = ?

Answers

Answer;

f (x) = 2x-4g (x) =x^2

Step-by-step explanation:

The solution is 9x² + 12x - 1

The composition function f ( g ( x ) ) is 9x² + 12x - 1

What is Composition of functions?

Evaluation of a function at the value of another function is known as Composition of function. A function composition is a process in which two functions, f and g, form a new function, h, in such a way that h(x) = g(f(x)). This signifies that function g is being applied to the function x. So, in essence, a function is applied to the output of another function.

Given data ,

Let the first function be represented as f ( x )

The value of f ( x ) = x² + 2x - 4

Let the second function be represented g ( x )

The value of g ( x ) = 3x + 1

Now , the composition function f ( g ( x ) ) is calculated by

Substitute the value of x as 3x + 1 , in f ( x ) , we get

f ( g ( x ) ) = f ( 3x + 1 )

f ( 3x + 1 ) = ( 3x + 1 )² + 2 ( 3x + 1 ) - 4

On simplifying the equation , we get

f ( 3x + 1 ) = ( 9x² + 6x + 1 ) + ( 6x + 2 ) - 4

f ( 3x + 1 ) = 9x² + 12x - 1

Therefore , the value of f ( 3x + 1 ) is 9x² + 12x - 1

Hence , the composition function f ( g ( x ) ) is 9x² + 12x - 1

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y=7x+8 can somebody help me

Answers

what’s the question ? do you need the slope or the y intercept ?

What is the measurement of angle D



HELP PLS

Answers

9514 1404 393

Answer:

  68°

Step-by-step explanation:

Alternate interior angles are congruent, so we have ...

  123° = d° +55°

  d = 123 -55 = 68

Angle D measures 68°.

_____

For those of you inclined to use this answer for other questions, here are the other angles in this figure.

  A = 55° . . . . alternate interior with 55°, so congruent

  B = C = 180° -123°

  B = C = 57°

Daniel debe $12.300 a Miguel y paga con un billete de $50.000 ¿cuanto dinero le devuelven ?​

Answers

Answer:

37,700

Step-by-step explanation:

I believe that you do 50,000 - 12,300. That would get you to your final answer of 37,700. So Miguel has to give 37,700 back to Daniel.

Hope this helped you!

Answer:

Miguel devuelve a Daniel $ 37.70

Step-by-step explanation:

50 - 12.3 = 37.7

Can someone help me, I forgot how to solve this

Answers

Answer:

y = mx + b

Step-by-step explanation:

what is domain and range because I got it wrong is not the right one ​

Answers

Answer:

You most likely got it wrong because you didn't plot all the points that are actually in the table, the domain and range are both right.

A car corporation produced 1980 fewer cars this month than last.
Write a signed number to represent this month's change in production.

Answers

Answer:

there was 1300 fewer cars so your answer would be -1300 :-)

Choose the equations that are equivalent. Select all that apply.
A. 52 = 8n +4
B. 42n + 1) = 52
C. 4 = 52 - 8n
D. 4n = 48

Answers

Answer:

A. 52 = 8n +4

C. 4 = 52 - 8n

Solve 11=h-14 please

Answers

Answer:

25

Step-by-step explanation:

25-14=11

Answer:

25

Step-by-step explanation:

11=25-14

Since 11+14 is 25 then h in 11=h-14 must be 25

What is the solution to the equation 1/3 n =6

Answers

Answer:

n=18

Step-by-step explanation:

Find the slope!!!
Quickly please

Answers

Answer:

the slope is m= 2

Answer:

2

Step-by-step explanation:

Slope is (y1 - y2) / (x1 - x2) for any 2 respective x's and y's.

For any of the points here, you get 2.

URGENT!!!!!!
Use scientific notation to estimate the number of inches in 1,225 miles. Include all calculations in your final answer.1 inch ≈ 1.578 × 10 -5 miles.

Answers

Answer: The number of inches in 1225 miles is [tex]7.763\times 10^7[/tex]

Step-by-step explanation:

Scientific notation is defined as the representation of expressing the numbers that are too big or too small and are represented in the decimal form with one digit before the decimal point times 10 raise to the power.

Example: 3000 is written as [tex]3.0\times 10^3[/tex]

Given : [tex]1.578\times 10^{-5}[/tex] miles = 1 inch

Thus 1 mile = [tex]\frac{1}{1.578\times 10^{-5}}=0.634\times 10^5[/tex] inches

1225 miles = [tex]\frac{0.634\times 10^5}{1}\times 1225=776.3\times 10^{5}=7.763\times 10^7[/tex] inches

Mrs. Brownstone brought 56 liters of juice for the fifth grade party. How many milliliters of juice did she bring?

Answers

Answer:

56000 milliliters

1 liter = 1000 milliliters

56(1000)=56000

Step-by-step explanation:

Mary has a large sum of money to deposit, but since she has heard many stories from her grandmother about the Great Depression, when many banks lost their customers’ deposits, she is worried that the bank might not keep her money safe. Give Mary some recommendations about what she can do to make sure that her money stays protected.

Answers

Mary should make sure to choose a bank that is FDIC insured. Furthermore, if she has more than maximum deposit insurance amount to deposit, she should spread her deposits out among several separate banks. These should be totally different banks, not simply different branches of the same bank. The FDIC will insure up to the maximum deposit insurance amount at each bank, even if the bank fails.

The masses of 4 containers loaded on a ship are 28 tonnes,45 tonnes,16.8tonnesand 48500kg .What is 5he total mass in tones?​

Answers

Step-by-step explanation:

first of all we have to change kg into ton= 48500kg into ton =53.462ton(48500/907.168)

after that we add all the weight of 4 container = 28+45+16.8+53.462

total will be his total mass of tones he had =143.262

It's urgent, Please answer, Make Sure you Round it

The first three terms of a sequence are given. Round to the nearest thousandth (if necessary).

460, 451,442

Find the 37th term.

Answers

Answer:

136

Step-by-step explanation:

This is an arithmetic sequence

The formula is an = a1 + f × (n-1)

n= the number we are trying to find = 37

a= the number in any given space on the sequence

a1= 460

f= the common difference between the numbers

f= -9 because you subtract 9 from each to get the number

a37= 460-9(37-1)

a37= 460-9(36)

a37= 460- 324

a37= 136

Given :

[tex] \\ [/tex]

The first three terms of a sequence are 460, 451, 442

[tex] \\ [/tex]

To Find :

[tex] \\ [/tex]

37th term of sequence = ?

[tex] \\ [/tex]

Solution :

[tex] \\ [/tex]

Clearly these three terms are making an arithmetic sequence, with :

First term, a = 460 Common difference, d = 451 - 460 = - 9

[tex] \\ [/tex]

Now, we have to find 37th term of sequence = [tex] \tt a_{37}[/tex]

[tex] \\ [/tex]

Now, we know that :

[tex] \large \underline{\boxed{\bf{a_{n} = a + (n-1)d}}}[/tex]

[tex] \\ [/tex]

[tex] \tt : \implies a_{37} = a + (37-1)d[/tex]

[tex] \tt : \implies a_{37} = a + 36d[/tex]

[tex] \\ [/tex]

Now, by substituting values of a and d :

[tex] \tt : \implies a_{37} = 460 + 36 \times (-9)[/tex]

[tex] \tt : \implies a_{37} = 460 - 324[/tex]

[tex] \tt : \implies a_{37} = 136[/tex]

[tex] \\ [/tex]

Hence, value of 37th term of given sequence is 136.

PLZ HELP ME PLZ I NEED IT

Answers

Answer:

Step-by-step explanation:

The intersection occurs at the point (3,-3) so those are the coordinates.

The age at which a person can be tried as an adult

Answers

Answer:

giyi

Step-by-step explanation:

Select the equivalent expression.
3-5 = ?

Answers

-2 !!!!!!!!!!!!!!!!!!!!!!!

Find the degree of the following polynomial:
7xy223 + 8y5 – 3x4 + 4

Answers

Answer:

224

Step-by-step explanation:

polynomial degree:224

leading term:7x^223

leading coefficient:7

X/4=8
Solve that using the opposite operation

Answers

Answer:

x = 32

Step-by-step explanation:

4 • (x/4) = 8 • 4

x = 32

Step-by-step explanation:

[tex]\qquad\sf\dashrightarrow x/4=8 [/tex]

[tex]\qquad\sf\dashrightarrow x=4×8 [/tex]

[tex]\qquad\sf\dashrightarrow x=32 [/tex]

a cylindrical tank has a radius of 3 m and a height of 12 m.
What is the volume of the tank?​

Answers

Answer:

Volume = 339.12 m^3

Step-by-step explanation:

Volume = Pi(r^2)(height)

Volume = 3.14(3^2)(12)

Volume = 339.12 m^3

write the following decimals in the form of p\ q= 0 and p,q are con-primes 1) 15.265





Answers

Given:

The decimal number is 15.265.

To find:

The decimals in the form of [tex]\dfrac{p}{q}[/tex] and p,q are co-primes.

Solution:

Let the decimal number be [tex]x=15.265[/tex].

It can be rewritten as

[tex]x=15.265\times \dfrac{1000}{1000}[/tex]

[tex]x=\dfrac{15265}{1000}[/tex]

[tex]x=\dfrac{5\times 3053}{5\times 200}[/tex]

Cancel out the common factors.

[tex]x=\dfrac{3053}{200}[/tex]

Here, p=3053 and q=200 and the HCF of (p,q) is 1. So, p and q are co-primes.

Therefore, the requited fraction form is [tex]\dfrac{3053}{200}[/tex].

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