Exponential and Logarithms Test Review

What is the inverse of an exponential function?

• Exponential function

• Power function

• Logarithmic function

• Base e function

Write in exponential form.

log₂32 = 5

• 2^-5 = 32

• 2³² = 5

• 2⁵ = 32

• 32⁵ = 2

Write in exponential form.

log₂(¹/₈) = -3

• 2^-3 = ¹/₈

• 2^1/8 = -3

• -3² = ¹/₈

• -3^1/8 = 2

Write in logarithmic form.

2^-4 = ¹/₁₆

• log₂(¹/₁₆) = -4

• log_-4(¹/₁₆) = 2

• log _-4 2 = ¹/₁₆

• log₂(-4) = ¹/₁₆

Write in logarithmic form.

5² = 25

• log₅2 = 25

• log₂25 = 5

• log₅25 = 2

• log₂₅5 = 2

Solve for x using the same base method:

(-3)^x = (-3)¹³

• -3

• 13

• X+13

• x-13

Solve for x using the same base metod:

27^2x = 3^x-7

• $-\frac{7}{3}$
  

• -1

• $-\frac{5}{7}$
  

• 
  

  $-\frac{7}{5}$

Solve for x using the same base method:

 $\frac{1}{4}=16^{\left(2x-5\right)}$  

•  $-\frac{11}{4}$  

• 8

•  $\frac{9}{4}$  

• 6

Evaluate the logarithm:

log₃81

• 4

• $\frac{1}{4}$

• -4

• $-\frac{1}{4}$

Evaluate the logarithm:
 $\log_6\left(\frac{1}{216}\right)$  

• 3

•  $\frac{1}{3}$  

•  $-\frac{1}{3}$  

• -3