Free Printable Exponential and Logarithmic Equations

Worksheets

Exponential and Logarithmic Equations

Total questions: 15

Worksheet time: 4hrs 31mins

Name

Class

Date

To solve, 16^5x = 64^x+7, what would be the correct set-up?

4^2(5x)=4^3(x+7) is one way to solve, which is another alternate set-up?

4^4(5x)=4^16(x+7)

8^2(5x)=8^8(x+7)

4^10x=4^3x+20

2^4(5x)=2^6(x+7)

Solve.

9(e^x)- 31 =23

x = 1.79

x = 4.21

x = -3.5

x = 1.27

Solve:

log(x) + log(x+3) = 1

-5, 2

5, -2

-5

Solve:

log₉(x)+log₉(x+2)=log₉(35)

-7

5, -7

-7, -13

To solve 8 = 2^5x+7, you could re-write 8 as what base?

Cannot be determined

Rewrite the exponential as a log.

2^3x+1= 12

ln(2)= 3x+1

log₂(12)= 3x+1

ln(6)=3x+1

log₁₂(2)= 3x+1

Solve:

log₂(x + 3)=5

x=2

x=29

x=7

x=32

Solve:

2log₆(x-8)=2

81/8

9969

Which is the correct way to rewrite,log₆(x-3)= 2, in order to solve.

6²= x-3

2⁶ = x - 3

ln(2) = x-3

e⁶ = x-3

10.

The first step to solve 8 + log 7 = 10 is...

Rewrite exponentially

Subtract 8 on both sides to isolate the log

Divide by 7 on both sides

11.

Determine the correct set-up for:

log(x) + log (x-9) = 18

log(x)/(x-9)=18

log(-7x)=18

log(x)+(x-9)=18

log x(x-9)=18

12.

Determine the correct set-up for:

log₄(x-1) - log₄(x+7) = log₄6

log₄(x-1)/(x+7)=log₄(6)

log₄(x-1)(x+7)=log₄(6)

log₄(x+7)/(x-1)=log₄(6)

(x-1)(x+7)=6

13.

Olivia would like to buy some new furniture for her home. She decides to buy the furniture on credit with 9.5% interest compounded quarterly. If she spent $7,400, how much total will she have paid after 8 years.

$15,415.94

$15,683.28

$15,927.56

$16,109.05

14.

Principal: $5000
Interest Rate: 3.75%
Time: 25 years
Compounded Monthly
State the future account balance.

$12712.31

$12,749.30

$12,657.59

$12550.84

15.

The function that models the decay of Carbon 14 is : $y=y_0e^{-0.0001216t}$ where y is the amount of Carbon 14 left after t years, and $y_0$ is the amount of Carbon 14 at t=0 .

How long before

y=\frac{1}{2}y_0

? (What is the half life of Carbon 14?) Round to the nearest whole year.

5700 years

-5700 years

$8.4\times10^{-5}$ years

$8.4\times10^5$ years

100 %

Exponential and Logarithmic Equations

Total questions: 15

Worksheet time: 4hrs 31mins

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