# How do you calculate Log_9 49?

Jun 1, 2016

$y = {\log}_{3} 7$

#### Explanation:

We know that $y = {\log}_{9} 49 \equiv {9}^{y} = 49$

Supposing you have for computational purposes the function

${\log}_{b}$, with $b$ the basis, you can proceed as
${\log}_{b} {9}^{y} = {\log}_{b} 49 \to y {\log}_{b} 9 = {\log}_{b} 49$

solving for $y$

$y = \frac{{\log}_{b} 49}{{\log}_{b} 9} = \frac{{\log}_{b} {7}^{2}}{{\log}_{b} {3}^{2}} = \frac{{\log}_{b} 7}{{\log}_{b} 3}$.

If you choose $b = 3$ as basis then the result will read

$y = {\log}_{3} 7$