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

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Answer 1 · 2015-08-01T19:14:26

$color(red)(x=16)$

$log(x+9) = log (2x-7)$

Convert the logarithmic equation to an exponential equation.

$10^( log(x+9)) = 10^( log (2x-7))$

Remember that $10^logx =x$ , so

$x+9 = 2x-7$

Move all terms to the right hand side.

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

Combine like terms.

$0 =x-16$

$x=16$

Check:

$log(x+9) = log (2x-7)$

If $x=16$

$log(16+9) = log (2(16)-7)$

$log25 = log (32-7)$

$log25 = log25$

$x=16$ is a solution.

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