5.3 Properties of Logs

log(4x)

• log4-logx

• log4+logx

• 4logx

• xlog4

log(xy²)

• logx+2logy

• logx+logy²

• logx-2logy

• logx+logy+log2

 $\log\left(\frac{x}{y}\right)$  

• logx+logy

• xlogy

• log(x-y)

• logx-logy

 $\log\left(\frac{m^3}{n}\right)$  

• logm-log3-logn

• 3logm+logn

• 3logm-logn

• 3log(m-n)

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

• ln2+2lnx+lny+4lnz

• ln2+2lnx+lny-4lnz

• 2ln(2xy)-4lnz

• 2ln2x+lny-4lnz

Use multiple log properties to write as a single log:
log₂x -  5log₂y

• log₂(x/y⁵)
• log₂(xy⁵)
• log₂(x/y)⁵
• log₂(x/5y)

• log (xy³)
• log (x⁶ − y³)
• log (x⁶/y³)
• log (x⁶ + y³)

• ln(wvu⁵)
• ln(u + v + w⁵)
• ln(uvw⁵)
• ln(uvw)⁵

Condense $15\ \log_5a\ +3\ \log_5b$  

•  $15\log_5ab$  

•  $\log_5\left(a^{15}b^3\right)$  

•  $\log_5\left(b^{15}a^3\right)$  

•  $45\log_5\left(ab\right)$  

 $4\log_4u-6\log_4v$  Condense

•  $\log_4\left(\frac{u}{v}\right)^{24}$  

•  $\log_4\left(\frac{u^6}{v^4}\right)^{ }$  

•  $\log_4\left(\frac{u^4}{v^6}\right)^{ }$  

•  $\log_4\left(\frac{v^6}{u^4}\right)^{24}$