Question

Solve the following equation:
$7^{\log x}-5^{\log x+1}={3.5}^{\log x-1}-{13.7}^{\log x-1}$

Answer 1

$7^{logx}-5^{logx+1}={3.5}^{logx-1}-{13.7}^{logx-1}\Rightarrow 7^{logx}-{5.5}^{logx}=3.{\frac{5}{5}}^{logx}-13.\frac{7^{logx}}{7}\Rightarrow \frac{20}{7}.7^{logx}=\left(\frac{28}{5}\right).5^{logx}\Rightarrow 7^{logx-2}=5^{logx-2}\Rightarrow logx-2=0\Rightarrow x=100$