M3H 16.1 Properties of Logs

Expland log(xy²)

• logx+2logy

• logx+logy²

• logx-2logy

• logx+logy+log2

Expand  $\log\left(\frac{m^3}{n}\right)$  

• logm-log3-logn

• 3logm+logn

• 3logm-logn

• 3log(m-n)

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

• ln2+2lnx+lny+4lnz

• ln2+2lnx+lny-4lnz

• 2ln(2xy)-4lnz

• 2ln2x+lny-4lnz

Condense: log16 + log2 - log8

• log4
• log8
• log10
• log24

condense log₂x - 5log₂y

• log₂(x/y⁵)

• log₂(xy⁵)

• log₂(x/y)⁵

• log₂(x/5y)

Condense  $\log_2\left(x+4\right)-\log_2\left(x^{2\ }-16\right)$  

•  $\log_2\left(x-4\right)$  

•  $\log_2\left(\frac{1}{x-4}\right)$  

•  $\log_2\left(\frac{1}{x+4}\right)$  

•  $\log_2\left(x+4\right)$  

Condense  $\frac{\ln9}{2}-\frac{\ln81}{4}+\ln e$  

• 0

• ln3

• 1

• 2

Evaluate:
log₄16

• 2
• 4
• 1/2
• -2

What would the change base look like for:

log₆ 48

• log 8

• $\frac{\log6}{\log48}$

• $\frac{\log48}{\log6}$

• ln 8

Use change of base property to write  $\frac{\log16}{\log3}$  as one Log

•  $\log_3\left(16\right)\$ 

•  $\log_{16}\left(3\right)$ 

•  $\log\left(13\right)$ 

•  $\log\left(19\right)$