How do you solve log_b(2)=0.24?

Jun 22, 2016

$b = 17.9594$

Explanation:

${\log}_{b} \left(2\right) = 0.24 \to 2 = {b}^{0.24}$

Applying ${\log}_{e}$ to both sides

${\log}_{e} 2 = 0.24 {\log}_{e} b$

then

${\log}_{e} b = {\log}_{e} \frac{2}{0.24} = 2.88811$

Finally

$b = {e}^{2.88811} = 17.9594$