Question

`log_(sqrt(2)) sqrt(8)` is equal to ______.

विकल्प

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Answer 1

`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