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Constant Function

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Question

The solution of ${(25)}^{x - 2} = {(125)}^{2 x - 4}$ is

A

\frac{3}{4}

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B

0

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C

2

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D

- 2

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Solution

The correct option is A $2$
$25^{x - 2} = (125)^{2 x - 4}$
$∴ 5^{2 (x - 2)} = 5^{3 (2 x - 4)}$
$∴ 2 (x - 2) = 3 (2 x - 4)$
$∴ 2 x - 4 = 6 x - 12$
OR $4 x = 8$
Only Possible When $x = 2$

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