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Q.

If f(x) is a function such that $f (xy) = f (x) + f (y) and f (2) = 1 then f (x) =$

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a

$\log_{2} x$

b

x²

c

$\log_{x} 2$

d

2^x

answer is C.

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Detailed Solution

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$f (x) = \log_{a} x \Rightarrow f (2) = \log_{a} 2 \Rightarrow 1 = \log_{a} 2 \Rightarrow a = 2 \Rightarrow f (x) = \log_{2} x$

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