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[tex]\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}}[/tex]



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