Question

Solve the following equation:
$5^{\log x}-3^{\log x-1}=3^{\log x+1}-5^{\log x-1}$

Answer 1

$5^{logx}-3^{logx-1}=3^{logx+1}-5^{logx-1}{\Rightarrow 5}^{logx}=a,3^{logx}=b$

Let, $a-\frac{b}{3}=3b-\frac{a}{5}$

$\Rightarrow \frac{6a}{5}=\frac{10b}{3}\Rightarrow 9a=25b\Rightarrow \frac{a}{25}=\frac{b}{9}\Rightarrow 5^{logx-2}=3^{logx-2}\Rightarrow logx-2=0\Rightarrow x=100.$