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

Explanation

8\({\frac{x}{2}}\) =   \(2^{\frac{3}{8}})(4^{\frac{3}{4}}\))
   applying the laws of indices.
(\(2^{3\times (\frac{x}{2})})  =  (2^{\frac{3}{8}})(2^{2\times (\frac{3}{4})}\))

\(2^{\frac{3x}{2}} = (2^{\frac{3}{8}})(2^{(\frac{3}{2})}\))

\(\frac{3x}{2} = \frac{3}{8} + \frac{3}{2}\)

\(\frac{3x}{2} =  \frac{3 + 12}{8}\)

\(\frac{3x}{2} =  \frac{15}{8}\) 

24x = 30

x =  \(\frac{30}{24} =  \frac{5}{4}\)