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5-log-x-x-log-2-find-x-




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

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