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Question
Find x so that `(2/9)^3 xx (2/9)^-6 = (2/9)^(2x - 1)`
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Solution
Given, `(2/9)^3 xx (2/9)^-6 = (2/9)^(2x - 1)`
Using law of exponents,
am × an = (a)m + n ...[∵ a is non-zero integer]
Then, `(2/9)^(3 - 6) = (2/9)^(2x - 1)`
⇒ `(2/9)^-3 = (2/9)^(2x - 1)`
On comparing, we get
–3 = 2x – 1
⇒ –2 = 2x
⇒ x = –1
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