`log(12x-11)=log(3x+13)` Solve the equation. Check for extraneous solutions.

`log(12x-11)=log(3x+13)`

Using the property of logarithmic equality,

`12x-11=3x+13`

`=>12x-3x=13+11`

`=>9x=24`

`=>x=24/9`

`=>x=8/3`

Let's plug back the solution in the equation to check the solution:

`log(12(8/3)-11)=log(3(8/3)+13)`

`log(4*8-11)=log(8+13)`

`log(32-11)=log(21)`

`log(21)=log(21)`

So, it's true.

Solution is `x=8/3`

Comments

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