Combine the logarithms first: log5(4x+3)-log5(x-1). Since it's subtract, divide the two.
log5((4x+3)/(x-1))=2
Make both sides the exponent of five. 5^log5 cancels out.
5^(log5(4x+3/x-1))=5^2
4x+3/x-1=25
Multiply both sides by (x-1) to get rid of it under 4x+3.
(x-1)4x+3/x-1=25(x-1)
4x+3=25x-25
Now subtract 4x from both sides AND add 25 to both sides. This way you'll have all the x's by itself.
28=21x
Divide both sides by 21.
28/21=x
x=1.33333333333...
