AnswersDHS Algebra 2 VSolving Exponential Equations by Rewriting the Base

Solving Exponential Equations by Rewriting the Base Answers

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1
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Solve: 43x = 42

A
Option
B
Option
C
Option
D
Option
2
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Solve: 62x - 3 = 6-2x+1

A
x = -1
B
x = 0
C
x = 1
D
x = 4
3

Solve: 3,125 = 5–10 + 3x x =

Answer:

5

4

Choose the correct equation.

A
(7) 3x = (73) 2x+1
B
(72) 3x = (73) 2x+1
C
(72) 3x = (74) 2x+1
5

To solve 493x = 3432x+1, write each side of the equation in terms of base .

Answer:

7

6

Solve:

Question illustration
A
a = –8
B
a = 0
C
a = 8
D
no solution
7

Rewrite the given equation so there is a single power of 5,000 on each side. Then, set the exponents equal to each other. Which equation shows the result?

Question illustration
A
2 = 1
B
z = 1
C
–4z + 2 = 1
D
–4z + 1 = 1
8

Solve:

Question illustration
A
Option
B
Option
C
Option
D
Option
9

Solve:

Question illustration
A
a = –3
B
a = 0
C
a = 3
D
no solution
10

Explain the error in the work shown. Find the correct answer.

Question illustration
Answer:

The error is that the bases were not rewritten to be the same. Since 16 = 4^2, the right side is (4^2)^(2a) = 4^(4a), not 2^(8a) when comparing with 4^-3. Thus -3 = 4a and the correct solution is a = -3/4.

11

Which of the following did you include in your explanation?

A
The bases were not the same when the exponents were set equal to each other.
B
16 should have been written as 4 squared.
C
The exponent on the right should be 4a instead of 8a.
D
The correct solution is .
12

Solve:

Question illustration
A
x = –1
B
x = 0
C
x = 1
D
no solution
13

Solve: 43x = 42

A
Option
Option A
B
Option
Option B
C
Option
Option C
D
Option
Option D
14

Solve: 3,125 = 5–10 + 3x x =

Answer:

5

15

To solve 493x = 3432x+1, write each side of the equation in terms of base .

Answer:

7

16

Choose the correct equation.

A
(7) 3x = (73) 2x+1
B
(72) 3x = (73) 2x+1
C
(72) 3x = (74) 2x+1
17

Solve:

Question illustration
A
a = –8
B
a = 0
C
a = 8
D
no solution
18

Rewrite the given equation so there is a single power of 5,000 on each side. Then, set the exponents equal to each other. Which equation shows the result?

Question illustration
A
2 = 1
B
z = 1
C
–4z + 2 = 1
D
–4z + 1 = 1
19

Solve:

Question illustration
A
x = –1
B
x = 0
C
x = 1
D
no solution
20

Solve:

Question illustration
A
Option
Option A
B
Option
Option B
C
Option
Option C
D
Option
Option D

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