How do you solve  14 ^(7x) = 21?

May 29, 2016

$x = \log \frac{21}{7 \log \left(14\right)} \approx 0.1648$

Explanation:

Take logs of both sides (any base) to get:

$\log \left(21\right) = \log \left({14}^{7 x}\right) = 7 x \log \left(14\right)$

Divide both ends by $7 \log \left(14\right)$ to find:

$x = \log \frac{21}{7 \log \left(14\right)} \approx 0.1648$