# How do you solve log (x+9) = log (2x-7)?

Aug 1, 2015

$\textcolor{red}{x = 16}$

$\log \left(x + 9\right) = \log \left(2 x - 7\right)$

Convert the logarithmic equation to an exponential equation.

${10}^{\log \left(x + 9\right)} = {10}^{\log \left(2 x - 7\right)}$

Remember that ${10}^{\log} x = x$, so

$x + 9 = 2 x - 7$

Move all terms to the right hand side.

$0 = 2 x - 7 - x - 9$

Combine like terms.

$0 = x - 16$

$x = 16$

Check:

$\log \left(x + 9\right) = \log \left(2 x - 7\right)$

If $x = 16$

$\log \left(16 + 9\right) = \log \left(2 \left(16\right) - 7\right)$

$\log 25 = \log \left(32 - 7\right)$

$\log 25 = \log 25$

$x = 16$ is a solution.