Question

Please friends help me with this logarithmic equation
How do I solve it?
Thanks you

Answer 1

`\displaystyle\\ \text{We use formula: } ~\log_a b+\log_a c=\log_a(b* 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*4x*5+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~~~|*(-1)\\\\ 48x=40 \\ \\ x = (40)/(48)=\boxed{(5)/(6)}`