Answer:
The solution is x = 32.
Step-by-step explanation:
To solve the logarithmic equation [tex]\log _4\left(\frac{x}{2}\right)=2[/tex] you must:
Use the logarithmic definition [tex]\mathrm{If}\:\log _a\left(b\right)=c\:\mathrm{then}\:b=a^c[/tex].
[tex]\log _4\left(\frac{x}{2}\right)=2\quad \Rightarrow \quad \frac{x}{2}=4^2[/tex]
Multiply both sides by 2
[tex]\frac{x}{2}\cdot \:2=4^2\cdot \:2[/tex]
Simplify
[tex]x=32[/tex]
