How do you solve 2 ^(4x)= 2.7?

Apr 20, 2018

$\textcolor{b l u e}{x = \ln \frac{2.7}{4 \ln \left(2\right)} \approx 0.3582398518}$

Explanation:

By the laws of logarithms:

${\log}_{a} \left({b}^{c}\right) = c {\log}_{a} \left(b\right)$

${2}^{4 x} = 2.7$

Taking natural logarithms of both sides:

$4 x \ln \left(2\right) = \ln \left(2.7\right)$

Divide by $4 \ln \left(2\right)$:

$x = \ln \frac{2.7}{4 \ln \left(2\right)} \approx 0.3582398518$