How do you solve 7.74^(x + 3) = 10.2?

Nov 22, 2015

I found: $x - 1.8651$

Explanation:

You can first take the natural log of both sides:

$\ln {\left(7.74\right)}^{x + 3} = \ln \left(10.2\right)$

Then you can use the property of logs that tells us that:

$\log {x}^{b} = b \log x$

and write:

$\left(x + 3\right) \ln \left(7.74\right) = \ln \left(10.2\right)$
rearrange:

$x + 3 = \frac{\ln \left(10.2\right)}{\ln} \left(7.74\right)$
$x = \frac{\ln \left(10.2\right)}{\ln} \left(7.74\right) - 3$
$x = 1.1348 - 3 = - 1.8651$