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Power Law

If 27x-1 = ...

Question

If $27^{x - 1} = 3^{x + 3}$ then $x =$

A

1

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B

4

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C

2

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D

3

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Solution

The correct option is B $3$
$27^{x - 1} = 3^{x + 3}$
$(3^{3})^{x - 1} = 3^{x + 3}$
$3^{3 x - 3} = 3^{x + 3}$
As the bases equal, exponents must be equal.
so $3 x - 3 = x + 3$
$3 x - x = 3 + 3$
$2 x = 6$
$x = \frac{6}{2} = 3$

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