# How do you solve Log_7(9-x)=2?

Nov 28, 2015

I found answer: $x = - 40$

#### Explanation:

To solve logarithmic equation, we switch it to exponential form

${\log}_{b} y = x$ $\leftrightarrow$ ${b}^{x} = y$

${\log}_{7} \left(9 - x\right) = 2$

$\left(9 - x\right) = {7}^{2}$ ; change to exponential form

$9 - x = 49$ ;

$- x = 40$ $\implies x = - 40$

Check:

log_7(9-(-40) =2

${\log}_{7} \left(49\right) = 2$

$2 = 2$