已知f(x)满足f(ab)=f(a)+f(b),且f(2)=p,f(3)=q,那么f(72)等于?
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已知f(x)满足f(ab)=f(a)+f(b),且f(2)=p,f(3)=q,那么f(72)等于?
已知f(x)满足f(ab)=f(a)+f(b),且f(2)=p,f(3)=q,那么f(72)等于?
已知f(x)满足f(ab)=f(a)+f(b),且f(2)=p,f(3)=q,那么f(72)等于?
f(72)=f(8)+f(9)=3f(2)+3f(3)=3p+3q
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
f(ab)=f(a)+f(b)
f(72)=f(2)+f(36)
f(36)=f(6)+f(6)
f(6)=f(2)+f(3)
综上得
f(72)=f(2)+f(36)=f(2)+f(6)+f(6)=f(2)+f(3)+f(2)+f(3)+f(2)
f(2)=p,f(3)=q
则得f(72)=3p+2q
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