Question

Solve the following equations.
$2^x\cdot 5^{x-1}=0.2\cdot {10}^{2-x}$

Answer 1

$2^x{.5}^{x-1}={\mathrm{0.2.10}}^{2-x}$

$2^x{.5}^{x-1}={2.10}^{1-x}$

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

comparing powers on both sides

$x=2-x⟹x=1$