Solve for $x$ :
$3^{4 x + 1} = (27)^{x + 1}$

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Solution

The correct option is A $2$
As given $3^{4 x + 1} = (27)^{x + 1}$
$\Rightarrow 3^{4 x + 1} = {(3^{3})}^{x + 1}$
$\Rightarrow 3^{4 x + 1} = (3^{3 \cdot (x + 1)})$
$\Rightarrow 3^{4 x + 1} = 3^{3 x + 3}$
Now we have equation for x
$\Rightarrow 4 x + 1 = 3 x + 3$
$\Rightarrow 4 x - 3 x = 3 - 1$
$\Rightarrow x = 2$

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