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Let f be a function defined on the set of all positive integers such that f( xy )=f( x )+f( y ) for all positive integers x , y . If f(12)=24 and f(8)=15 , the value of f(48) is

Options

  1. A31
  2. B32
  3. C33
  4. D34

Correct answer

D. 34

Step-by-step solution

f(x y)=f(x)+f(y) f(x)= _ a x So, f(12)=24 _ a 12=24 12=a²⁴ & f(8)=15 _ a 8=15 8=a¹⁵ 2=a⁵ So, f(48)= _ a 48= _ a 12+ _ a 4= _ a 12+ _ a 2²=24+2 5=34

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