We have
[tex]\ln \mleft(-x+1\mright)-ln\mleft(3x+5\mright)=ln\mleft(-6x+1\mright)[/tex]We need to simplify by applying logarithms rules
[tex]\ln \mleft(-x+1\mright)=ln\mleft(-6x+1\mright)+ln\mleft(3x+5\mright)[/tex][tex]ln(-x+1)=\ln ((-6x+1)(3x+5))[/tex]Then we apply the exponential on both sides
[tex]-x+1=(-6x+1)(3x+5)[/tex]We simplify
[tex]18x^2+26x-4=0[/tex]Then we solve the second equation degree with the general formula
[tex]x_{1,2}=\frac{-b\pm\sqrt[]{b^2-4ac}}{2a}[/tex]where
a=18
b=26
c=-4
we substitute the values
[tex]x_{1,2}=\frac{-26\pm\sqrt[]{(26)^2-4(18)(-4)}}{2(18)}[/tex][tex]x_{1,2}=\frac{-26\pm2\sqrt[]{241}}{36}[/tex]We reduce and the solution is
[tex]x_1=\frac{-13+\sqrt[]{241}}{18}=0.14[/tex][tex]x_2=\frac{-13-\sqrt[]{241}}{18}=-1.58[/tex]ANSWER
–1.58 or 0.14
