Given the equation:
[tex]4\ln \mleft(5x\mright)+5=2[/tex]We will find the value of (x) as follows:
a) subtract 5 from both sides
[tex]\begin{gathered} 4\ln \mleft(5x\mright)+5-5=2-5 \\ 4\ln \mleft(5x\mright)=-3 \end{gathered}[/tex]b) Divide both sides by 4
[tex]\ln (5x)=-\frac{3}{4}[/tex]c) Taking the exponential of both sides to remove ln
[tex]5x=e^{-\frac{3}{4}}[/tex]Finally, divide both sides by 5
[tex]x=\frac{1}{5}e^{-\frac{3}{4}}\approx0.09447[/tex]So, the answer will be x = 0.09447
