Question

Solve the following equation:
$5^{x-1}={10}^x\cdot 2^{-x}\cdot 5^{x+1}$

Answer 1

$5^{x-1}={10}^x{.2}^{-x}{.5}^{x+1}$

$5^{x-1}=5^x{.5}^{x+1}$

$5^{x-1}=5^{2x+1}$

$\therefore x=-2$