How do you solve 4 ^ (4x-6) = 39?

Apr 21, 2016

$x = \frac{1}{4} \left(\ln \frac{39}{\ln} 4 + 6\right) \approx 2.16$

Explanation:

$\ln {4}^{4 x - 6} = \ln 39$

$\left(4 x - 6\right) \ln 4 = \ln 39$

$4 x - 6 = \ln \frac{39}{\ln} 4$

$4 x = \ln \frac{39}{\ln} 4 + 6$

$x = \frac{1}{4} \left(\ln \frac{39}{\ln} 4 + 6\right) \approx 2.16$