Lesson 5.2 Properties of Logs

 $\ln\left(\frac{2x^2y}{z^4}\right)$  

• ln2+2lnx+lny+4lnz

• ln2+2lnx+lny-4lnz

• 2ln(2xy)-4lnz

• 2ln2x+lny-4lnz

Expand.

• 1/3 log x + log y + log z
• 1/3 log x + 1/3 log y + 1/3 log z
• 1/3 log x - 1/3 log y - 1/3 log z
• 3 log x + 3 log y + 3 log z

Condense into a single logarithm.
 $\log_43+2\log_4x+3\log_4y$  

•  $\log_4\left(3x^2y^3\right)$  
  

•  $\log_4\left(18xy\right)$  
  

•  $\log_4\left(3xy\right)$   
  

•  $\log_4\left(8xy\right)$  

Expand into multiple logarithms.   $\log\left(xyz^3\right)$  

•  $\log x+\log y+3\log z$  

•  $3\log x+3\log y+3\log z$  

•  $\log x-\log y-3\log z$  

•  $\left(\log x\right)\left(\log y\right)\left(3\log z\right)$  

Expand into multiple logarithms.   $\log_5\frac{a^4b}{c^7}$  

•  $\log_5\left(4a\right)+\log_5b-\log_5\left(7c\right)$  

•  $4\log_5a+\log_5b-7\log_5c$  

•  $\log x-\log y-3\log z$  

•  $\left(\log x\right)\left(\log y\right)\left(3\log z\right)$  

Use properties of Logs to write  $\log_3\left(4\right)-\log_3\left(x\right)+\log_3\left(y\right)$  

as one Log

•  $\log_3\left(\frac{4x}{y}\right)\$ 

•  $\log_3\left(4xy\right)$ 

•  $\log_3\left(\frac{4}{xy}\right)$ 

•  $\log_3\left(\frac{4y}{x}\right)$ 

• 6log₈(xyz)
• log₈(x) - log₈(y) - 6log₈(z)
• log₈(x) + log₈(y) - log₈(z)
• log₈(x) + log₈(y) + 6log₈(z)