Question

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

log3(2) and log3(5).

log3(18/25)

Answer 1

`\begin{array}{llll} \textit{Logarithm of exponentials} \\\\ \log_a\left( x^b \right)\implies b\cdot \log_a(x) \end{array}~\hfill \begin{array}{llll} \textit{Logarithm of rationals} \\\\ \log_a\left( (x)/(y)\right)\implies \log_a(x)-\log_a(y) \end{array} \\\\\\ \begin{array}{llll} \textit{logarithm of factors} \\\\ \log_a(xy)\implies \log_a(x)+\log_a(y) \end{array} \\\\[-0.35em] ~\dotfill`

`\log_3\left( \cfrac{18}{25} \right)\implies \log_3(18)~~ - ~~\log_3(25)\implies \log_3(2\cdot 3\cdot 3)~~ - ~~\log_3(5^2) \\\\\\\ [\log_3(2)+\log_3(3)+\log_3(3)]~~ - ~~2\log_3(5) \\\\\\\ [\log_3(2)+1+1]~~ - ~~2\log_3(5)\implies 2+\log_3(2)-2\log_3(5)`