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

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.