# How do you solve 3^(x-2)=13^(4x)?

Feb 5, 2016

Take natural logarithm both side

$\ln \left({3}^{x - 2}\right) = \ln \left({13}^{4 x}\right)$

$x \ln \left(3\right) - 2 \ln \left(3\right) = 4 x \ln \left(13\right)$

$2 \ln \left(3\right) = x \ln \left(3\right) - 4 x \ln \left(13\right)$

$2 \ln \left(3\right) = x \left(\ln \left(3\right) - 4 \ln \left(13\right)\right)$

$\frac{2 \ln \left(3\right)}{\ln \left(3\right) - 4 \ln \left(13\right)} = x$