Solving Exponentials Using Change of Base

Solving Exponentials Using Change of Base

Presentation

•

Mathematics

•

9th - 11th Grade

•

Hard

Created by

Joseph Anderson

FREE Resource

4 Slides • 6 Questions

1

Lesson 6.7 Solving Exponential Equations

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2

Type 1: Same base on both sides

Ignore the base
Set the exponents equal to each other
Solve

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3

Multiple Choice

$2^x=2^{\left(5x-80\right)}$

1

$x=-11$

2

$x=20$

3

$x=4$

4

$x=-16$

4

What if they don't have the same base?

Can you change one of them to have the same base as the other?

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5

Multiple Choice

$7^3=49^{\left(x+5\right)}$

1

$x=5$

2

$x=-2$

3

$x=-\frac{7}{2}$

6

Type 2: Exponent only on 1 side

Change to logarithmic form
Use change of base formula to solve

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7

Multiple Choice

$10^x=1500$

1

$x=150$

2

$x=10$

3

$x=3.18$

8

Multiple Choice

$5^{4x}=2115$

1

$x=19.03$

2

$x=1.19$

3

$x=4.78$

4

$x=12.98$

9

Multiple Choice

$10^x+8=1008$

1

$x=10$

2

$x=3$

3

$x=8$

4

$x=100$

10

Multiple Choice

$7^{\left(x+10\right)}-8=6$

1

$x=-7.374$

2

$x=-8.643$

3

$x=-7.360$

4

$x=-8.853$

pattern-tertiary

Lesson 6.7 Solving Exponential Equations

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