Question

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

Answer 1

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

Answer 2

f(72)=f(8)+f(9)=f(2)+f(2)+f(2)+f(3)+f(3)=3p+2q

Answer 3

由题意
f(6)=f(2)+f(3)=p+q
f(12)=f(2)+f(6)=2p+q
f(72)=f(6)+f(12)=3p+2q