# Solve 10^(12x+2) = (10^10)^(2x-1) ?

$x = \frac{3}{2}$
${\log}_{10} \left(12 x + 2\right) = {\log}_{10} \left(\left(2 x - 1\right) \cdot 10\right) \to 12 x + 2 = 10 \left(2 x - 1\right)$
Solving for $x$ gives
$x = \frac{3}{2}$ which is feasible