# How do you solve 11.3^(2x – 1) = 15.7?

Apr 28, 2016

I found: $x = 1.0678$

#### Explanation:

Here I would use the natural log on both sides and one property of logs (about the exponent of the argument):

I write:

$\textcolor{red}{\ln} {11.3}^{2 x - 1} = \textcolor{red}{\ln} 15.7$

then:

$\left(2 x - 1\right) \ln \left(11.3\right) = \ln \left(15.7\right)$

rearrange:
$2 x - 1 = \frac{\ln \left(15.7\right)}{\ln \left(11.3\right)}$
$2 x = \frac{\ln \left(15.7\right)}{\ln \left(11.3\right)} + 1$
$x = \frac{\frac{\ln \left(15.7\right)}{\ln \left(11.3\right)} + 1}{2} = 1.0678$