Question

What is the exact value of x?

5*21^5x = 16

Answer 1

`\bf \textit{Logarithm of exponentials} \\\\ log_a\left( x^b \right)\implies b\cdot log_a(x) \\\\[-0.35em] \rule{34em}{0.25pt}`

`\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( (16)/(5)\right)~~}{\log(21)}\implies x=\cfrac{~~\log\left( (16)/(5)\right)~~}{5\log(21)} \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ ~\hfill x\approx 0.0764094095937~\hfill`

Answer 2

X=log 3.2/5 log 21

Explanation:

X=0.0764094