Question

If $4^x - 3^{x - \frac{1}{2}} = 3^{x + \frac{1}{2}} - 2^{2x - 1}$, then the value of $x$ is:

• A. $\dfrac{7}{2}$
• B. $\dfrac{5}{2}$
• C. $\dfrac{1}{2}$
• D. $\dfrac{3}{2}$

Hint:

For exponential equations with fractional exponents, try substituting simple rational values.

Answer 1

The Correct Option is D

Let’s test $x = \dfrac{3}{2}$: \[ 4^{3/2} = 8,\quad 3^{1} = 3,\quad 3^{2} = 9,\quad 2^{2} = 4 \] LHS: $4^{3/2} - 3^{1} = 8 - 3 = 5$
RHS: $3^{2} - 2^{2} = 9 - 4 = 5$
LHS = RHS ⇒ $x = \dfrac{3}{2}$ satisfies the equation.