Question Number 199486 by hardmath last updated on 04/Nov/23
$$\mathrm{Solve}:\:\:\:\mathrm{100}^{\boldsymbol{\mathrm{x}}} \:=\:\mathrm{200} \\ $$
Answered by cortano12 last updated on 04/Nov/23
$$\mathrm{log}\:_{\mathrm{10}} \left(\mathrm{100}^{\mathrm{x}} \right)=\:\mathrm{log}\:_{\mathrm{10}} \left(\mathrm{200}\right) \\ $$$$\:\:\mathrm{2x}\:=\:\mathrm{2}+\mathrm{log}\:_{\mathrm{10}} \left(\mathrm{2}\right) \\ $$$$\:\:\:\mathrm{x}=\mathrm{1}+\mathrm{log}\:_{\mathrm{10}} \left(\sqrt{\mathrm{2}}\:\right) \\ $$
Answered by Skabetix last updated on 04/Nov/23
$${xln}\left(\mathrm{100}\right)={ln}\left(\mathrm{200}\right) \\ $$$${x}=\frac{{ln}\left(\mathrm{200}\right)}{{ln}\left(\mathrm{100}\right)}=\frac{{log}\left(\mathrm{200}\right)}{\mathrm{2}} \\ $$