Question

8. Solve the following equation: log4 (2x - 3) = log4 (5x + 1)

Answer 1

Given the logarithm equation as shown below

`\log _4(2x-3)=\log _4(5x+1)`

To solve the equation above, we will divide both sides by the log to the base of 4 and solve the resulting algebraic equation

`(\log_4(2x-3))/(\log_4)=(\log _4(5x+1))/(\log _4)`
`\begin{gathered} 2x-3=5x+1 \\ \text{Collect like terms} \\ 2x-5x=1+3 \\ -3x=4 \end{gathered}`

Divide both sides by -3

`\begin{gathered} (-3x)/(-3)=(4)/(-3) \\ x=-(4)/(3) \end{gathered}`

Hence, the solution of the equation is x= -4/3