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JEE Previous Year Question

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

Topic: JEE PYQ

Answer: D. Full step-by-step solution below.

A $\frac{7}{2}$
B $\frac{5}{2}$
C $\frac{1}{2}$
D $\frac{3}{2}$

Correct answer: D

Solution

(d) 4^{x} - 3^{x - \frac{1}{2}} = 3^{x + \frac{1}{2}} - 2^{2 x - 1} 4^{x} + 2^{2 x - 1} = 3^{x + \frac{1}{2}} + 3^{x - \frac{1}{2}} \Rightarrow 4^{x} + \frac{4 ^{x}}{2} = 3^{x} (3 + \frac{1}{3}) \frac{3}{2} 4^{x} = 3^{x} \cdot \frac{4}{3} (\frac{3}{4})^{x} = \frac{3 3}{8} = \frac{3 ^{3/2}}{4 ^{3/2}} \Rightarrow (\frac{3}{4})^{x} = (\frac{3}{4})^{3/2} ∴ x = \frac{3}{2}

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