Understanding exponential and logarithmic functions

Use multiple log properties to write as a single log:

3log₂x - log₂y + log₂z

• $\log_2\ \frac{x}{yz}$

• $\log_2\ \frac{x^3}{yz}$

• $\log_2\ \frac{x^3z}{y}$

• $\log_2\ \frac{xz}{y}$

Expand the expression: log₅3x/2

• log₅3 - log₅x - log₅2

• log₅3 + log₅x - log₅2

• log₅2 - log₅3

• log₅3 + log₅x + log₅2

Condense:  $\log\left(5x+2\right)\ -\ \log3\ -\ \log x$  Rewrite:  $\log\ \left(5x\ +\ 2\right)\ -\ \left(\log_{\ }3\ +\ \log x\right)$  Use product and quotient rules

 $\log\left(5x+2\right)\ \div\log\left(\ 3x\right)$  

•  $\log\left(\frac{3x}{5x\ +\ 2}\right)$  

•  $\log\left(\frac{5x\ +\ 2}{3x}\right)$  

•  $\log\left(3x\left(5x+2\right)\right)$  

•  $\log\left(\frac{5x\ +\ 2}{3\ -\ x}\right)$  

• 1

• -1

• 25

• 1/25

Expand the logarithm

• A

• B

• C

• D

Mathematical Equivalence

ON

Evaluate the following logarithm:

 $\log_8\sqrt{8}=$  

• -¹/₂

• -1

• 1

• ¹/₂

• None of these

Evaluate  $\log_93$  without using a calculator.

•  $\frac{1}{2}$  

•  $-2$  

•  $\frac{1}{3}$  

•  $-\frac{1}{2}$  

Condense

• A

• B

• C

• D