\(\displaystyle\\
\text{We use formula: } ~\log_a b+\log_a c=\log_a(b\times c)\\\\
2\log_3(4x-5)=\log_3(4x+5)+\log_3(4x-3)\\\\
\log_3(4x-5)^2=\log_3[(4x+5)(4x-3)]\\\\
(4x-5)^2=(4x+5)(4x-3)\\\\
16x^2-2\times4x\times5+25=16x^2+20x-12x-15\\\\
16x^2-40x+25=16x^2+8x-15\\\\
\underbrace{16x^2}-\underline{\underline{40x}}+\underline{25}-\underbrace{16x^2}-\underline{\underline{8x}}+\underline{15}=0\\\\
-48x+40=0\\\\
-48x = -40~~~|\times(-1)\\\\
48x=40 \\ \\
x = \frac{40}{48}=\boxed{\frac{5}{6}}\)
