Exponentials & Logs

Rewrite as an exponential: log₂8 = 3

• 3² = 8

• 2³ = 8

• 2⁸ = 3

• 8³ = 2

Rewrite as an exponential:  $\log_7\left(\frac{1}{49}\right)=-2$  

•  $7^{\frac{1}{49}}=-2$  

•  $\left(\frac{1}{49}\right)^{-2}=7$  

•  $7^{-2}=\frac{1}{49}$  

•  $\left(-2\right)^7=\frac{1}{49}$  

Rewrite as an exponential:  $\log_93=\frac{1}{2}$  

•  $9^{\frac{1}{2}}=3$  

•  $3^{\frac{1}{2}}=9$  

•  $9^3=\frac{1}{2}$  

•  $\left(\frac{1}{2}\right)^9=3$  

Rewrite as a log: y = 7^x

• log₇(x) = y

• log_y(7) = x

• log_x(y) = 7

• log₇(y) = x

Rewrite as a log: x = 11^y

• log₁₁(y) = x

• log_y(11) = x

• log₁₁(x) = y

• log_x(y) = 11

Rewrite as a log: 7⁰ = 1

• log₇(1) = 0

• log₀(7) = 1

• log₇(0) = 1

• log₁(0) = 7

What is the base for the following log:

y = log (x)

• 1

• 0

• 10

• 2

Find x: log₂(32) = x

• x = 5

• x = 16

• x = 4

• x = 6

Find x: log₅(x) = 4

• x = 20

• x = 25

• x = 625

• x = 125

Find x: log_x(25) = 2

• x = 1

• x = 12.5

• No Solution

• x = 5