# How do you solve e^(3x)=20?

May 14, 2016

$\approx 1$

#### Explanation:

${e}^{3 x} = 20$

Taking ${\log}_{e}$ on both sides we have
${e}^{3 x} = 20$

$\implies {\log}_{e} {e}^{3 x} = {\log}_{e} 20$

$\implies \left(3 x\right) {\log}_{e} e = {\log}_{e} 20 \text{ }$ using formula ${\log}_{e} {m}^{n} = n {\log}_{e} m$

$\implies \left(3 x\right) = {\log}_{e} 20 \text{ }$ since ${\log}_{e} e = 1$

$\implies x = {\log}_{e} \frac{20}{3} \approx \frac{3}{3} = 1$