Properties of Logs

 $\log\left(\frac{x}{y}\right)$  

• logx+logy

• xlogy

• log(x-y)

• logx-logy

Condense: log16 + log2 - log8

• log4
• log8
• log10
• log24

log(4x)

• log4-logx

• log4+logx

• 4logx

• xlog4

Using the change of base property, rewrite log₂31

• log(2) / log(31)

• log(2/31)

• log(31)/log(2)

• log(31/2)

log(xy²)

• logx+2logy

• logx+logy²

• logx-2logy

• logx+logy+log2

 $\log\left(\frac{m^3}{n}\right)$  

• logm-log3-logn

• 3logm+logn

• 3logm-logn

• 3log(m-n)

Simplify log₄4^3x

• 3x
• 3
• 4
• 4^3x

Condense into a single logarithm.
 $\log_25+\log_29+\log_2w$  

•  $\log_2\left(14w\right)$  
  

•  $\log_2\left(45w\right)$  
  

•  $\log_2\left(\frac{14}{w}\right)$   
  

•  $\log_2\left(14+w\right)$  

Condense: log₂6+log₂3=

• log₂18

• log₂2 = 1

• log₂3

• log₂9

log(3x)²

• 2log(3+x)

• 2log3+logx

• log3+2logx

• 2(log3+logx)