# How do you solve 3*6^(9r)=92.3?

Sep 25, 2016

$r = 0.21249$

#### Explanation:

$3 \cdot {6}^{9 r} = 92.3$

divide both sides by 3:
$\implies {6}^{9 r} = \frac{92.3}{3}$
$\implies {6}^{9 r} = 30.77$

take the log of both sides:
$\implies \log {6}^{9 r} = \log 30.77$
$\implies 9 r \log 6 = \log 30.77$

divide both sides by $\log 6$
$\implies 9 r \cancel{\log} \frac{6}{\cancel{\log}} 6 = \log \frac{30.77}{\log} 6$

$\implies 9 r = 1.91239$ (use calculator)

divide both sides by 9
$\implies \frac{\cancel{9} r}{\cancel{9}} = \frac{1.91239}{9} = 0.21249$

Hence, $r = 0.21249$