Logarithms help please - AS Level Maths?

log_2 = log base 2

3 = log_2(5x-7) - log_2(2x-5)

3 = log_2[(5x-7)/(2x-5)]

(5x-7)/(2x-5) = 2^3 = 8

5x-7 = 8(2x-5)

5x-7 = 16x-40

-11x = - 33

x = 3

Checking:

3 + log_2(2*3-5) = log_2(5*3-7)

3 + log_2(1) = log_2(8)

3 + 0 = 3

You know from the domain that x > 5/2 so ignore 5/8 which appears to have been plucked out of thin air

3 = log(base 2)8
So, you get
8(2x-5) = 5x-7
11x = 33
x = 3 <==Answer

This is gibberish just quit man !