Question

ln(3x-1) - ln(x+2) = 2ln5

Answer 1

ln(3x-1) - ln(x+2) = 2ln5 , where x > -2

ln((3x-1)/(x+2)) = ln 5^2
(3x-1)/(x+2) = 25
25x + 50 = 3x - 1
22x = -51
x = -51/22

but that would make ln(x+2) undefined.

there is no solution