Logarithms! How do i solve: log(5x-1)-log(2x-3)=2

Simple log problem from analysis...i dont understand what i am doing wrong. Here is my work:

log(5x-1)-log(2x-3)=2
log(5x-1)/(2x-3)=2
(5x-1)/(2x-3)=2^10
10x^2-2x-15x+3=200x-300
10x^2-17x+303=0
realllllly messed up-_-

First, in your third line

(5x-1)/(2x-3)=2^10

you seem to have mixed up the base (which is 10) with the logarithm (2). It should read

(5x-1)/(2x-3)=10^2

however, that could be just a typing error, since you have corrected it in the continuation.

Your crucial error is in the next line.

From

(5x-1)/(2x-3) = 200

when you multiply both sides by (2x - 3) you get

(5x - 1) (2x - 3)
------------------- = 200 (2x - 3)
. . . (2x - 3)

which simplifies to just

(5x - 1) = 200 (2x - 3)

Otherwise, everything is fine.

OKAY. HERE IS MY SOLUTION.
LOG((5X-1)/(2X-3))=2
(5X-1)/(2X-3)=(10°2)=100
5X-1=100(2X-3)
5X-1=200X-300
195X=299
X=23/15
HOPE THIS HELPED.
(HINT: U DONT HAVE TO MULTIPLY 5X-1 AND 2X-3)