Question

Use the properties of logarithms to write the logarithm in terms of

log5(2) and log5(3).

log5(12)

Answer 1

`\begin{array}{llll} \textit{logarithm of factors} \\\\ \log_a(xy)\implies \log_a(x)+\log_a(y) \end{array} ~\hspace{4em} \begin{array}{llll} \textit{Logarithm of exponentials} \\\\ \log_a\left( x^b \right)\implies b\cdot \log_a(x) \end{array} \\\\[-0.35em] ~\dotfill\\\\ \log_5(12)\implies \log_5(4\cdot 3)\implies \log_5(2^2\cdot 3) \\\\\\ \log_5(2^2)~~ + ~~\log_5(3)\implies 2\log_5(2)~~ + ~~\log_5(3)`