Logarithm 2: Identities

Logarithmic identities

Identity 1

•  $\log_5\left(3\times2\right)=\ \log_5\ 3+\ \log_{5\ }2$  

•  $\log_a\left(xy\right)=\ \log_a\ x+\ \log_{a\ }y$  

• Proof:  raise the base 'a' to these powers and due the monotonity of the expoential function

Identity 2

•  $\log_2\left(12\div4\right)=\ \log_2\ 12+\ \log_{2\ }4$  

•  $\log_a\left(\frac{x}{y}\right)=\log_ax-\log_ay$  

• Proof:  raise the base 'a' to these powers and due the monotonity of the expoential function

Identity 2

•  $\log_5\left(3^2\right)=\ 2\log_5\ 3$  

•  $\log_a\left(x^k\right)=k\log_ax$  

• Proof:  raise the base 'a' to these powers and due the monotonity of the expoential function