Given the logarithm equation as shown below
[tex]\log _4(2x-3)=\log _4(5x+1)[/tex]
To solve the equation above, we will divide both sides by the log to the base of 4 and solve the resulting algebraic equation
[tex]\frac{\log_4(2x-3)}{\log_4}=\frac{\log _4(5x+1)}{\log _4}[/tex][tex]\begin{gathered} 2x-3=5x+1 \\ \text{Collect like terms} \\ 2x-5x=1+3 \\ -3x=4 \end{gathered}[/tex]
Divide both sides by -3
[tex]\begin{gathered} \frac{-3x}{-3}=\frac{4}{-3} \\ x=-\frac{4}{3} \end{gathered}[/tex]
Hence, the solution of the equation is x= -4/3
