How do you solve 2*7^(6x) -8 =16 and find any extraneous solutions?

Aug 20, 2016

$\therefore x = \frac{1.277}{6} = 0.2128$

Explanation:

$2 \cdot {7}^{6 x} - 8 = 16$

$\therefore 2 \cdot {7}^{6 x} = 16 + 8 = 24$

$\therefore {7}^{6 x} = \frac{24}{2} = 12$

$\therefore 6 x = {\log}_{7} 12$

By the Change of Base Rule, we have,

$6 x = {\log}_{10} \frac{12}{\log} _ 10 7 = \frac{1.0792}{0.8451} = 1.277$

$\therefore x = \frac{1.277}{6} = 0.2128$