[tex]\bf \textit{Logarithm of exponentials} \\\\ log_a\left( x^b \right)\implies b\cdot log_a(x) \\\\[-0.35em] \rule{34em}{0.25pt}[/tex]
[tex]\bf 5\cdot 21^{5x}=16\implies 21^{5x}=\cfrac{16}{5}\implies \stackrel{\textit{taking \underline{log } to both sides}}{\log\left( 21^{5x} \right)=\log\left( \cfrac{16}{5} \right)} \\\\\\ 5x\log(21)=\log\left( \cfrac{16}{5} \right)\implies 5x=\cfrac{~~\log\left( \frac{16}{5}\right)~~}{\log(21)}\implies x=\cfrac{~~\log\left( \frac{16}{5}\right)~~}{5\log(21)} \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ ~\hfill x\approx 0.0764094095937~\hfill[/tex]
