Properties of Logarithms

Product Property    log_{b}(m \cdot n)= log_{b}(m) + log_{b}(n)
Quotient Property   log_{b}\left(\frac{m}{n} \right) = log_{b}(m)-log_{b}(n)
Power Property      log_{b}\left( m^{n} \right) = n \cdot log_{b}(m)

 

hmm, they look kinda like the properties of exponents…

Examples: Expand the logarithmic expressions

Product Property:

    \[log_{4}(2 \cdot 16)=\]

Quotient Property:

    \[log_{10}\left(\frac{90}{7} \right)=\]

Power Property:

    \[log_{17}(14^3)=\]