Let `f` be a funcation defined on the set of all positive integers such that `f (x) +f(y) ` for all postive integers x,y,if f (12) =24 and f(8) =15 the value of f(48) is

Options

A. 31
B. 32
C. 33
D. 34

Answer

d

Explanation

f (x y) = f(x) +f(y)
f(x) =`log_(a)x`
so , f(12) =24
`Rightarrow log_(a) 12=24`
`Rightarrow 12 = a^(24)& f(8)=15`
`Rightarrow log_(a) 8 =15`
`Rightarrow 8=a^(15) Rightarrow 2=a^(5) `
So, f(48) = `log_(a)48=log_(a) 12 + log_(a)4`
`log_(a)12 + log_(a)2^(2)`
24+2.5
34