ALg2_5.19

Rewrite log₃t = 5 in exponential form.

• 5^t=3
• log₃5 = log₃t
• t⁵=3
• 3⁵=t

Expand  $\log_4\left(6y\right)$  

•  $\log_4\left(6\right)\ +\ \log_4\left(y\right)$ 

•  $\log_4\left(6\right)\ -\ \log_4\left(y\right)$ 

•  $y\log_4\left(6\right)\$ 

•  $\log_4\left(\frac{6}{y}\right)\$ 

Expand  $\log_4\left(3xy\right)$  

•  $\log_4\left(3\right)\ +\ \log_4\left(x\right)-\ \log_4\left(y\right)$ 

•  $3\log_4\left(x\right)\ +\ 3\log_4\left(y\right)$ 

•  $\log_4\left(3\right)\ +\ \log_4\left(x\right)+\ \log_4\left(y\right)\$ 

•  $4\log\left(3\right)\ +\ 4\log\left(x\right)+\ 4\log\left(y\right)\$ 

Expand  $\log_2\left(3y^2\right)$  

•  $\log_2\left(3\right)\ +\ \log_2\left(y\right)$ 

•  $2\log_2\left(3\right)\ +\ 2\log_2\left(y\right)$ 

•  $\log_2\left(3\right)\ +\ 2\log_2\left(y\right)$ 

•  $\log_2\left(\frac{3}{y^2}\right)\$ 

Use properties of Logs to write  $2\log_3\left(4\right)$  

as one Log

•  $\log_3\left(12\right)\$ 

•  $\log_3\left(8\right)$ 

•  $\log_3\left(16\right)$ 

•  $\log_3\left(6\right)$ 

Use properties of Logs to write  $2\log_3\left(x\right)+\log_3\left(y\right)$  

as one Log

•  $\log_3\left(2xy\right)\$ 

•  $\log_3\left(x^2y\right)$ 

•  $\log_3\left(xy\right)^2$ 

•  $2\log_3\left(xy\right)$ 

Evaluate log₈ 8

• 8
• -1
• 0
• 1

Evaluate:
log₄16

• 2
• 4
• 1/2
• -2

Rewrite in logarithmic form:

6² = 36

• log₆ 2 = 36

• log₆ 36 = 2

• ln 36 = 2

• 6³⁶ = 2

Rewrite in logarithmic form:

5³ = 125

• log ₅ 125 = 3

• log ₃ 125 = 5

• log ₅ 3 =125

• log₁₂₅ 3 = 5