Question Number 16973 by tawa tawa last updated on 29/Jun/17
$$\mathrm{5}^{\mathrm{log}\left(\mathrm{x}\right)} \:=\:\mathrm{x}^{\mathrm{log}\left(\mathrm{2}\right)} ,\:\:\:\:\:\mathrm{find}\:\:\mathrm{x}. \\ $$
Answered by mrW1 last updated on 29/Jun/17
![log (x) log (5)=log (2) log (x) log (x)[ log (5)−log (2)]=0 ⇒log (x)=0 ⇒x=1](Q16978.png)
$$\mathrm{log}\:\left(\mathrm{x}\right)\:\mathrm{log}\:\left(\mathrm{5}\right)=\mathrm{log}\:\left(\mathrm{2}\right)\:\mathrm{log}\:\left(\mathrm{x}\right) \\ $$$$\mathrm{log}\:\left(\mathrm{x}\right)\left[\:\mathrm{log}\:\left(\mathrm{5}\right)−\mathrm{log}\:\left(\mathrm{2}\right)\right]=\mathrm{0} \\ $$$$\Rightarrow\mathrm{log}\:\left(\mathrm{x}\right)=\mathrm{0} \\ $$$$\Rightarrow\mathrm{x}=\mathrm{1} \\ $$
Commented by tawa tawa last updated on 29/Jun/17
$$\mathrm{God}\:\mathrm{bless}\:\mathrm{you}\:\mathrm{sir}. \\ $$