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Question
`log_(sqrt(2)) sqrt(8)` is equal to ______.
Options
3
4
16
5
MCQ
Fill in the Blanks
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Solution
`log_(sqrt(2)) sqrt(8)` is equal to 3.
Explanation:
Let `x = log_(sqrt(2)) sqrt(8)`.
Then `(sqrt2)^x = sqrt(8)`.
Write both as powers of 2:
`(2^(1/2))^x = 2^(3/2)`
⇒ `2^(x/2) = 2^(3/2)`
⇒ `x/2 = 3/2`
⇒ x = 3
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