Solve for x : $4^{2 x + 3} = 16^{1 - 2 x}$

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Solution

We have,
$4^{2 x + 3} = 16^{1 - 2 x}$
$4^{2 x + 3} = 4^{2 (1 - 2 x)}$

On equating both power, we get
$2 x + 3 = 2 (1 - 2 x)$
$2 x + 3 = 2 - 4 x$
$6 x = - 1$
$x = - \frac{1}{6}$

Hence, this is the answer.

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