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nth Term of an AP

If 27x=32x+...

Question

If $27^{x} = 3^{2 x + 3}$ then the value of $x =$

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Solution

given, $27^{x} = 3^{2 x + 3}$

${(3^{3})}^{x} = 3^{2 x + 3}$

$3^{3 x} = 3^{2 x + 3}$

Since bases are the same we can equate the powers.

$\Rightarrow 3 x = 2 x + 3$

$\Rightarrow 3 x - 2 x = 3$

$∴ x = 3$

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