Question

Is
`(log11)/(log5) = (ln11)/(ln5)` ? Why or why not?

Answer 1

`\textit{Logarithm Change of Base Rule} \\\\ \log_a b\implies \cfrac{\log_c b}{\log_c a}\qquad \qquad c= \begin{array}{llll} \textit{common base for }\\ \textit{numerator and}\\ denominator \end{array} \\\\[-0.35em] ~\dotfill\\\\ \log_5(11)\implies \cfrac{\log_(10)(11)}{\log_(10)(5)}\implies \stackrel{\textit{\Large both are equal}}{\boxed{\cfrac{\log(11)}{\log(5)}}\implies \cfrac{\log_(e)(11)}{\log_(e)(5)}\implies \boxed{\cfrac{\ln(11)}{\ln(5)}}}`