# How do you solve 12^x=14^(3x)?

Aug 5, 2015

I found: $x = 0$

#### Explanation:

Take the natural log (ln) on both sides:
$\ln {12}^{x} = \ln {14}^{3 x}$
use the property that:
$\ln {x}^{a} = a \ln x$ to get:
$x \ln 12 = 3 x \ln 14$
$x \ln 12 - 3 x \ln 14 = 0$
so:
$x \left(\ln 12 - 3 \ln 14\right) = 0$

this is true only if $x = 0$