# How do you solve 3^(n+3)=14.5?

Apr 23, 2018

$n \approx 2.43115$

#### Explanation:

${3}^{x + 3} = 14.5$

$\Rightarrow {3}^{n} \cdot {3}^{3} = 14.5$

$\Rightarrow {3}^{n} \cdot 27 = 14.5$

$\Rightarrow {3}^{n} = \frac{14.5}{27}$

and based on the definition of logs
$\Rightarrow n = {\log}_{3} \left(\frac{14.5}{27}\right)$

This can be evaluated with a calculator or spreadsheet function
(for my spread sheet this would look like $= \log \left(14.5 \text{/} 27 , 3\right)$)
to obtain the approximation:
$n \approx 2.4311499$