Boom, Crash! With Logs

Boom, Crash! With Logs

This will help you practice expanding and condensing with logs!

Submit your work in Classroom

Be sure you show your steps on your paper, and submit this in Classroom when you are done to receive full credit.

Multiple Choice

Expand the Log completely and simplify if possible.  $\log_{ }\left(\frac{\sqrt{x}}{z^5y}\right)$  

•  $\frac{1}{2}\log x\ -5\log z-\log y$ 

•  $\log\ x^{\frac{1}{2}\ }-\log\ z^5+\log\ y$  

•  $\log\ \sqrt{x}-\log z^5+y^{ }$   

•  $10\log\ x-z+y$  

Multiple Choice

Condense $15\ \log_5a\ +3\ \log_5b$  

•  $15\log_5ab$  

•  $\log_5\left(a^{15}b^3\right)$  

•  $\log_5\left(b^{15}a^3\right)$  

•  $45\log_5\left(ab\right)$  

Multiple Choice

 $\log_{16}\left(\frac{4x}{y^2}\right)$  

Expand the expression:

•  $\frac{1}{2}+\log_{16}x+2\log y$  
  

•  $\frac{1}{2}+\log_{16}x-2\log_{16}y$  
  

•  $4+\log_{16}x-\log_{16}y^2$  
  

• Not here

Multiple Choice

 $\log\left(\frac{x}{y}\right)$  

• logx+logy

• xlogy

• log(x-y)

• logx-logy

Multiple Choice

Expand: $\log_9\left(27x^3y\right)$  

•  $3\log_9\left(27x\right)+\log_9y$  
  

•  $\frac{3}{2}+3\log_9x+\log_9y$  
  

•  $\log_93+\log_927+\log_9x+\log_9y$  
  

• Not here

Multiple Select

Which one(s) below would condense to...

 $\log_2\left(\frac{8a^3}{b}\right)$  

•  $3+3\log_2a-\log_2b$  

•  $6\log_2a-\log_2b$  

•  $\log3+\log_2a^3-\log_2b$  

•  $\log_2a^3+3-\log_2b$  

Multiple Select

Which one(s) would condense to... $\log_4\left(\frac{a^4b}{12b^2}\right)$  

•  $4\log_4\left(ab\right)-3-2\log_4b$  

•  $4\log_4a+\log_4b-\log_412+\log_4b^2$  

•  $4\log_4a-\log_412-\log_4b$  

•  $\log_4\left(a^4b\right)-\log_4\left(12b^2\right)$  

Multiple Choice

Condense! $\frac{2}{3}\log_327-2\log_4x+\frac{1}{2}\log_4y$ 

•  $\log_4\left(\frac{16\sqrt{y}}{x^2}\right)$  

•  $\log_4\left(\frac{8y}{x^2}\right)$  

•  $\log_4\left(\frac{3\sqrt{y}}{x^2}\right)$  

•  $\log_4\left(\frac{6}{x^2y}\right)$