Home » If 8(frac{x}{2}) = (2(frac{3}{8}))(4(frac{3}{4})), find x

If 8(frac{x}{2}) = (2(frac{3}{8}))(4(frac{3}{4})), find x

If 8^(frac{x}{2}) = (2^(frac{3}{8}))(4(frac{3}{4})), find x

A.
(frac{3}{8})
B.
(frac{3}{4})
C.
(frac{4}{5})
D.
(frac{5}{4})

Correct Answer: Option D

Explanation

8^(frac{x}{2}) = 2^(frac{3}{8})2^{2 x (frac{3}{4})} 2^{(frac{3x}{2})}
= 2^(frac{3}{4})^{(frac{3x}{2})}
= (frac{15}{8})
(frac{2 times 15}{3 times 8}) = (frac{5}{4})