`log_5(2x-7)=log_5(3x-9)` Solve the equation. Check for extraneous solutions.

Expert Answers

An illustration of the letter 'A' in a speech bubbles

`log_5(2x-7)=log_5(3x-9)`

Using one to one property of logarithms,

`2x-7=3x-9`

`=>2x-3x=-9+7`

`=>-x=-2`

`=>x=2`

Let's plug back the solution in the equation,

`log_5(2*2-7)=log_5(3*2-9)`

`log_5(-3)=log_5(-3)`

However logarithm of negative number is undefined,

So the solution is extraneous.

See eNotes Ad-Free

Start your 48-hour free trial to get access to more than 30,000 additional guides and more than 350,000 Homework Help questions answered by our experts.

Get 48 Hours Free Access
Approved by eNotes Editorial