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Question
Find x.
`(2/5)^(2x + 6) xx (2/5)^3 = (2/5)^(x + 2)`
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Solution
We have, `(2/5)^(2x + 6) xx (2/5)^3 = (2/5)^(x + 2)`
Using law of exponents,
am × an = (a)m + n ...[∵ a is non-zero integer]
Then, `(2/5)^(2x + 6 + 3) = (2/5)^(x + 2)`
On comparing powers of `(2/5)`, we get
2x + 6 + 3 = x + 2
⇒ 2x + 9 = x + 2
⇒ x = –7
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