# How do you solve ln(9r+1)=ln(r^2+9)?

Sep 3, 2016

The Soln. is $r = 8 , 1$.

#### Explanation:

Since, $\ln$ function is $1 - 1$,

$\ln \left(9 r + 1\right) = \ln \left({r}^{2} + 9\right)$

$\Rightarrow 9 r + 1 = {r}^{2} + 9 , \mathmr{and} , {r}^{2} - 9 r + 8 = 0$

$\Rightarrow \left(r - 8\right) \left(r - 1\right) = 0$

$\Rightarrow r = 8 , r = 1$.

Both these roots satisfy the given eqn. Hence,

The Soln. is $r = 8 , 1$.