Answer:
[tex]\large\boxed{x=\dfrac{5}{2}=2\dfrac{1}{2}}[/tex]
Step-by-step explanation:
[tex]Domain:\ 4x>0\to x>0\\\\Use:\ \log_ab=c\iff a^c=b\ for\ a>0\ \wedge\ a\neq1\ \wedge\ b>0\\\\\log(x)=\log_{10}(x)\\=============================\\\\2+3\log(4x)=5\qquad\text{subtract 2 from both sides}\\\\3\log(4x)=3\qquad\text{divide both sides by 3}\\\\\log(4x)=1\iff4x=10^1\\\\4x=10\qquad\text{divide both sides by 4}\\\\x=\dfrac{10}{4}\\\\x=\dfrac{10:2}{4:2}\\\\x=\dfrac{5}{2}\\\\x=2\dfrac{1}{2}\in D[/tex]
