Answer:
x = 698.771
step-by-step explanation:
[tex]\sf \rightarrow \log _{2x}\left(5^{\dfrac{3}{2}}\right)=\dfrac{1}{3}[/tex]
apply ln rules
[tex]\sf \rightarrow \dfrac{\ln \left(5^{\dfrac{3}{2}}\right)}{\ln \left(2x\right)}=\dfrac{1}{3}[/tex]
cross multiply
[tex]\sf \rightarrow \ln \left(5^{\dfrac{3}{2}}\right)\cdot \:3=\ln \left(2x\right)\cdot \:1[/tex]
simplify using calculator
[tex]\sf \rightarrow 7.24247 = ln(2x)[/tex]
shift sides
[tex]\sf \rightarrow e^{7.24247 }= 2x[/tex]
divide both sides by 2
[tex]\sf \rightarrow 698.771= x[/tex]
