How do you solve 6^x=72?

Dec 2, 2016

x≈2.387

Explanation:

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

$\textcolor{\mathmr{and} a n \ge}{\text{Reminder }} \textcolor{red}{\overline{\underline{| \textcolor{w h i t e}{\frac{2}{2}} \textcolor{b l a c k}{\log {x}^{n} = n \log x} \textcolor{w h i t e}{\frac{2}{2}} |}}}$
$\textcolor{w h i t e}{\times \times \times x} \text{Applies to logs in any base.}$

Take the natural log ( ln) of both sides.

$\Rightarrow \ln {6}^{x} = \ln 72$

Using the above law.

$x \ln 6 = \ln 72$

rArrx=ln72/ln6≈2.387" to 3 decimal places"