Question
Solve for $x : 3^{4x + 1}= (27)^{x + 1}$
✓
Answer
$3^{4x + 1}= (27)^{x + 1}$
$\Rightarrow 3^{4x + 1} = (3^3)^{x + 1}$
$\Rightarrow 3^{4x + 1} =( 3^3)^{x + 1}$
We know that if bases are equal, the powers are equal
$\Rightarrow 4x + 1 = 3x + 3$
$\Rightarrow 4x - 3x = 3 - 1$
$\Rightarrow x = 2.$
$\Rightarrow 3^{4x + 1} = (3^3)^{x + 1}$
$\Rightarrow 3^{4x + 1} =( 3^3)^{x + 1}$
We know that if bases are equal, the powers are equal
$\Rightarrow 4x + 1 = 3x + 3$
$\Rightarrow 4x - 3x = 3 - 1$
$\Rightarrow x = 2.$
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