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Q.

The equation $18^{4 x - 3} = {(54 \sqrt{2})}^{3 x - 4}$ has a solution which is

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a

an even integer

b

none of these

c

coprime with 5

d

a prime number

answer is A, C.

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Detailed Solution

${(18)}^{4 x - 3} = {(18^{\frac{3}{2}})}^{\frac{3 x}{4}}$

$\begin{array}{l} \Rightarrow 4 x - 3 = \frac{3}{2} (3 x - 4) \\ x = 6. \end{array}$

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The equation 184x−3=(542)3x−4 has a solution which is