Evaluating Logarithms

Rewrite the following expression in exponential form:

 $\log_5\left(\frac{1}{25}\right)=-2$  

•  $\left(-2\right)^5=\frac{1}{25}$  

•  $5^{\frac{1}{25}}=-2$  

•  $5^{-2}=\frac{1}{25}$  

•  $\left(\frac{1}{25}\right)^{-2}=5$  

•  $\left(-2\right)^{\frac{1}{25}}=5$  

Rewrite the following expression in logarithmic form:

 $8^{\frac{2}{3}}=4$  

•  $\log_8\left(\frac{2}{3}\right)=4$  

•  $\log_4\left(8\right)=\frac{2}{3}$  

•  $\log_{\frac{2}{3}}\left(4\right)=8$  

•  $\log_8\left(4\right)=\frac{2}{3}$  

Which of the following logarithms = 2? Select all that apply:

• $\log_5\left(10\right)$

• $\log\left(100\right)$

• $\ln\left(e^2\right)$

• $\log_2\left(2\right)$

• $\log_{\frac{1}{2}}\left(\frac{1}{4}\right)$

What number must fill in the blank to make this equation true?

 $\log_3\left(\ \ \ \ \ \ \ \ \ \ \ \right)=-3$  

What number must fill in the blank to make this equation true?

 $\log_{343}\left(\ \ \ \ \ \ \ \ \ \ \ \ \ \ \right)=\frac{1}{3}$  

Evaluate the following logarithm:

 $\log_m\left(m^{12}\right)=?$  

• 1

• 12

•  $m^{12}$  

• 0

Evaluate:

 $\log_6\left(1\right)=?$  

Evaluate:

 $\log_2\left(16\right)=?$  

Evaluate:  $\log_{81}\left(27\right)=?$  

 $\log_4\left(\frac{1}{16}\right)=?$  

Evaluate: