Question Number 172074 by Mikenice last updated on 23/Jun/22
$${solve}: \\ $$$$\mathrm{5}^{{logx}} =\mathrm{50}−{x}^{{log}\mathrm{5}} \\ $$
Answered by aleks041103 last updated on 23/Jun/22
$$\mathrm{5}^{{logx}} =\mathrm{10}^{{log}\mathrm{5}\:{logx}} =\left(\mathrm{10}^{{logx}} \right)^{{log}\mathrm{5}} ={x}^{{log}\mathrm{5}} \\ $$$$\Rightarrow\mathrm{2}.\mathrm{5}^{{logx}} =\mathrm{50} \\ $$$$\Rightarrow\mathrm{5}^{{logx}} =\mathrm{25}=\mathrm{5}^{\mathrm{2}} \Rightarrow{logx}=\mathrm{2} \\ $$$$\Rightarrow{x}=\mathrm{100} \\ $$