# How do you solve 3^x-2=11?

Sep 7, 2016

x≈2.335

#### Explanation:

We use the $\textcolor{b l u e}{\text{law of logarithms}}$

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

${3}^{x} - 2 = 11 \Rightarrow {3}^{x} = 13$

Now take the ln of both sides. I have used ln but a log to any base can be used.

$\Rightarrow \ln {3}^{x} = \ln 13$

Using the above law allows us to obtain x as a multiplier.

xln3=ln13rArrx=(ln13)/(ln3)≈2.335