JAMB 1997 · UME · Q6

If $8^{\frac x2} = 2^{\frac38} \times 4^{\frac34}$ , find $x$ .

Worked solution (try it first)

Write everything as a power of 2: $8^{\frac x2} = (2^3)^{\frac x2}$
$= 2^{\frac{3x}{2}}$ and $4^{\frac34} = (2^2)^{\frac34}$
$= 2^{\frac32}$ .
Right side: add the powers, $\frac38 + \frac32 = \frac38 + \frac{12}{8}$
$= \frac{15}{8}$ .
Equate the powers: $\frac{3x}{2} = \frac{15}{8}$ , so $x = \frac{15}{8} \times \frac23 = \frac54$ , option D.