Question

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

Answer 1

`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.