已知函数f（x）满足f(ab)=f(a)+f(b),且f(2)=p,f(3)=q,f(72)=?

题目

已知函数f（x）满足f(ab)=f(a)+f(b),且f(2)=p,f(3)=q,f(72)=?
·········

答案

f(ab)=f(a)+f(b)
f(72)=f(2×36)
=f(2)+f(36)
=f(2)+f(2×18)
=f(2)+f(2)+f(18)
=f(2)+f(2)+f(2×9)
=f(2)+f(2)+f(2)+f(3×3)
=f(2)+f(2)+f(2)+f(3)+f(3)
=3p+2q