M3H 16.1 Properties of Logs

Expland log (xy²)

• log x + 2log y

• log x + log y²

• log x - 2log y

• log x + log y + log 2

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

• log m - log 3 - log n

• 3log m + log n

• 3log m - log n

• 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)

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)\$ 

•  $\log_{16}\left(3\right)$ 

•  $\log\left(13\right)$ 

•  $\log\left(19\right)$ 

Use the change of base formula if necessary to evaluate the following logarithms to three decimal places.
 $\log_37$