Solving Log and Exponential Equations

Rewrite the logarithm in exponential form:
 $\log_yx=10$  

•  $y^{10}=x$  

•  $x^{10}=y$  

•  $10^y=x$  

•  $y^x=10$  

Rewrite the logarithm in exponential form:
 $\log_x25=3$  

•  $x^3=25$  

•  $3^x=25$  

•  $25^3=x$  

•  $25^x=3$  

Write the following logarithm as an exponential:
 $\ln\left(5\right)=x$  

•  $5^x$  

•  $e^x=5$  

•  $e^5=x$  

•  $x^5=2.71$  

Mr. Peake puts $1000 in an investment account. The account grows annually by 11% per year. How much time will go by before the account reaches a balance of $15,000?

• 25.9 years

• 26.2 years

• 26.4 years

• 26.8 years

The formula $N=N_o\ e^{1.5t}$  can be used to model the continuous spread of poison ivy leaves in a forest. If t represents time in weeks and the initial cluster of poison ivy has 8 leaves, how long will it take for there to be 7000 poison ivy leaves in the forest?

• 4.6 weeks

• 5.0 weeks

• 12.2 weeks

• 10.8 weeks

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

• 8

• 4

• 2

• 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 for x:

4^x = 17

• 0.489

• 2.552

• 0.893

• 2.044

Solve the equation for x.

• x = 2
• x = 3
• x = 8
• x = 64

7ⁿ⁺¹⁰- 8 = 6

• -7.374
• -8.643
• -7.360
• -8.853