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

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Solution

We have $3^{4 x + 1} = {(27)}^{x + 1}$
$\Rightarrow 3^{4 x + 1} = {(3^{3})}^{x + 1}$
By using law $(a^{m})^{n} = a^{m \times n}$
$\Rightarrow 3^{4 x + 1} = 3^{3 x + 3}$
Base are same so we get an equation
$\Rightarrow 4 x + 1 = 3 x + 3$
$\Rightarrow 4 x - 3 x = 3 - 1 \Rightarrow x = 2$

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