# How do you solve 3e^x+1=5?

Oct 20, 2016

x≈0.2877" to 4 dec. places"

#### Explanation:

Begin by expressing the equation in terms of ${e}^{x} .$

$3 {e}^{x} = 4 \Rightarrow {e}^{x} = \frac{4}{3}$

Take ln (natural logarithm) of both sides.

$\Rightarrow \ln {e}^{x} = \ln \left(\frac{4}{3}\right)$

$\textcolor{\mathmr{and} a n \ge}{\text{Reminder }} \textcolor{red}{\overline{\underline{| \textcolor{w h i t e}{\frac{2}{2}} \textcolor{b l a c k}{\log {a}^{x} \Leftrightarrow x \log a} \textcolor{w h i t e}{\frac{2}{2}} |}}}$

$\Rightarrow x {\cancel{\ln e}}^{1} = \ln \left(\frac{4}{3}\right)$

rArrx=ln(4/3)≈0.2877" to 4 dec. places"