First slide

Theory of expressions

Question

If $4^{x} - 3^{x - 1 / 2} = 3^{x + 1 / 2} - 2^{2 x - 1}$ then value
of $x$ is equal to

Moderate

A

5/2
B

2
C

3/2
D

1

Solution

$4^{x} - 3^{x - 1 / 2} = 3^{x + 1 / 2} - 2^{2 x - 1}$
$\begin{array}{l} \Rightarrow 4^{x} + 2^{2 x - 1} = 3^{x + 1 / 2} + 3^{x - 1 / 2} \\ \Rightarrow 4^{x} + \frac{4^{x}}{2} = 3^{x} \sqrt{3} + \frac{3^{x}}{\sqrt{3}} \\ \Rightarrow (\frac{3}{2}) 4^{x} = (\frac{4}{\sqrt{3}}) 3^{x} \\ \Rightarrow {(\frac{4}{3})}^{x} = \frac{2}{3} \times \frac{4}{\sqrt{3}} = \frac{8}{3 \sqrt{3}} = {(\frac{2}{3^{1 / 2}})}^{3} = {(\frac{4}{3})}^{3 / 2} \\ \Rightarrow x = 3 / 2 \end{array}$

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