ln(3x+1)/ln(5x-1)=2
ln(3x+1)=2*ln(5x-1)
ln(3x+1)=ln{(5x-1)^2}
3x+1=(5x-1)^2
3x+1=(5x)^2-2*(5x)+1^2
3x+1=25x^2-10x+1
25x^2-13x=0
x(25x-13)=0
x=0 or x=13/25 (Discard x=0 because it does not satisfy the equation)
Therefore x = 13/25=0.52
CHECK TO SEE IF IT SATISFY THE EQUATION
ln(3*.52+1)/ln(5*.52) = 2
ln(2.56)/ln(1.6) = 2
2 = 2
It checks out