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Question
Find the value of x so that (2–1 + 4–1 + 6–1 + 8–1)x = 1
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Solution
We have, (2–1 + 4–1 + 6–1 + 8–1)x = 1
Using law of exponents,
`a^-m = 1/a^m` ...[∵ a is non-zero integer]
Then, `(1/2 + 1/4 + 1/6 + 1/8)^x = 1`
⇒ `((12 + 6 + 4 + 3)/24)^x = 1` ...[∵ LCM of 2, 4, 6 and 8 = 24]
⇒ `(25/24)^x = 1`
This can be possible only if x = 0. Since, a0 = 1. ....[Law of exponents]
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