# How do you solve  3.14159^x=4?

Jul 21, 2016

$x = \ln \frac{4}{\ln} \left(3.14159\right) = {\log}_{3.14159} \left(4\right)$

#### Explanation:

We will use the property of logarithms that $\ln \left({a}^{x}\right) = x \ln \left(a\right)$

With that:

${3.14159}^{x} = 4$

$\implies \ln \left({3.14159}^{x}\right) = \ln \left(4\right)$

$\implies x \ln \left(3.14159\right) = \ln \left(4\right)$

$\therefore x = \ln \frac{4}{\ln} \left(3.14159\right)$

Note that this is eqivalent to the base $3.14159$ log of $4$, a result we could have also found by taking the base $3.14159$ log of both sides and applying ${\log}_{a} \left({a}^{x}\right) = x$