How do you solve for x in 25 = 3 ^ (x/100)?

Jun 26, 2016

$x = 293.02$

Explanation:

$25 = {3}^{\frac{x}{100}}$

i.e. $\log 25 = \log \left({3}^{\frac{x}{100}}\right) = \frac{x}{100} \log 3$

Hence $\frac{x}{100} = \log \frac{25}{\log} 3$ and

$x = 100 \times 2 \log \frac{5}{\log} 3 = 200 \times \frac{0.6990}{0.4771}$

or $x = 293.02$