Inverse Functions and Logarithms

Rewrite log₂8 = 3 in exponential form

• 2⁸ = 3

• 2³ = 8

• 3² = 8

• 8³ = 2

Rewrite 3⁴ = 81 in logarithmic form.

• log₃4 = 81

• log₈₁3 = 4

• log₃81 = 4

• log₄81 = 3

Evaluate.

log₂32

• 5

• 3

• -5

• 4

• A

• B

• C

• D

Are these inverse functions?

• no

• yes

• no way to tell

Are the blue and red graphs inverse functions?

• yes

• no

• no way to tell

Find the value of x:

8^x=2^x-4

• x = -2

• x = 2

• x = -4

• x = 4

 $f\left(x\right)=\frac{x-6}{7}$  

Find the inverse function.

•  $f^{-1}\left(x\right)=7x+6$  

•  $f^{-1}\left(x\right)=6x+7$  

•  $f^{-1}\left(x\right)=\frac{7x}{6}$  

•  $f^{-1}\left(x\right)=7x-6$  

Find the inverse function:

f(x) = log₄x

• f ^-1(x) = 4^x

• f ^-1(x) = 4x

• f ^-1(x) = log_x4

• f ^-1(x) = x⁴

Find the value of x:

6^2x+1 = 6^3x-4

• x = 5

• x = 1

• x = -1

• x = -5