If $4^{2 x + 2} = 64$ , then calculate the value of $x$ .

\frac{1}{2}

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1

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\frac{3}{2}

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2

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Solution

The correct option is B $\frac{1}{2}$
Given is $4^{2 x + 2} = 64$
LHS:
$\Rightarrow 4^{2 x + 2} = (2^{2})^{2 x + 2} \Rightarrow 2^{4 x + 4}$
RHS:
$\Rightarrow 64 = 2^{6}$

Now, LHS $=$ RHS
$\Rightarrow 2^{4 x + 4} = 2^{6}$
As bases are equal, so powers must be equal,
$\Rightarrow 6 = 4 x + 4$
$\Rightarrow 4 x = 2 \Rightarrow x = \frac{1}{2}$

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