The logarithmic equation given is,
[tex]\log _4\left(11x\right)=2[/tex]
Apply log rules
[tex]\log_4\left(11x\right)=\log_42^4[/tex]
Cancel out the log₄
[tex]11x=2^4[/tex]
Solve for x
[tex]\begin{gathered} 11x=16 \\ Divide\text{ both sides by 11} \\ \frac{11x}{11}=\frac{16}{11} \\ x=\frac{16}{11}=1\frac{5}{11} \end{gathered}[/tex]
Hence, the solution set is
[tex]x=\frac{16}{11}or1\frac{5}{11}[/tex]
