Question

Simplify using the log properties then evaluate.
log2 5+ log2 6.4

Answer 1

`\begin{array}{llll} \textit{logarithm of factors} \\\\ \log_a(xy)\implies \log_a(x)+\log_a(y) \end{array} \\\\\\ \begin{array}{llll} \textit{Logarithm Cancellation Rules} \\\\ \stackrel{\textit{we'll use this one}}{log_a a^x = x}\qquad \qquad a^(log_a x)=x \end{array} \\\\[-0.35em] ~\dotfill\\\\ \log_2(5)+\log_2(6.4)\implies \log_2( ~~(5)(6.4) ~~ )\implies \log_2(32) \\\\\\ \log_2(2^5)\implies \text{\LARGE 5}`