已知函数f(x)满足f(ab)=f(a)+f(b),且f(2)=p,f(3)=q,则f(72)等于——A p+q B 3p+2q C 2p+3q D p³+q³ 答案是什么不重要 我要解题过程或解题思路
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![已知函数f(x)满足f(ab)=f(a)+f(b),且f(2)=p,f(3)=q,则f(72)等于——A p+q B 3p+2q C 2p+3q D p³+q³ 答案是什么不重要 我要解题过程或解题思路](/uploads/image/z/8825548-4-8.jpg?t=%E5%B7%B2%E7%9F%A5%E5%87%BD%E6%95%B0f%EF%BC%88x%EF%BC%89%E6%BB%A1%E8%B6%B3f%EF%BC%88ab%EF%BC%89%3Df%EF%BC%88a%EF%BC%89%2Bf%EF%BC%88b%EF%BC%89%2C%E4%B8%94f%EF%BC%882%EF%BC%89%3Dp%2Cf%EF%BC%883%EF%BC%89%3Dq%2C%E5%88%99f%EF%BC%8872%EF%BC%89%E7%AD%89%E4%BA%8E%E2%80%94%E2%80%94A+p%2Bq+B+3p%2B2q+C+2p%2B3q+D+p%26%23179%3B%2Bq%26%23179%3B+%E7%AD%94%E6%A1%88%E6%98%AF%E4%BB%80%E4%B9%88%E4%B8%8D%E9%87%8D%E8%A6%81+%E6%88%91%E8%A6%81%E8%A7%A3%E9%A2%98%E8%BF%87%E7%A8%8B%E6%88%96%E8%A7%A3%E9%A2%98%E6%80%9D%E8%B7%AF)
已知函数f(x)满足f(ab)=f(a)+f(b),且f(2)=p,f(3)=q,则f(72)等于——A p+q B 3p+2q C 2p+3q D p³+q³ 答案是什么不重要 我要解题过程或解题思路
已知函数f(x)满足f(ab)=f(a)+f(b),且f(2)=p,f(3)=q,则f(72)等于——
A p+q B 3p+2q C 2p+3q D p³+q³ 答案是什么不重要 我要解题过程或解题思路
已知函数f(x)满足f(ab)=f(a)+f(b),且f(2)=p,f(3)=q,则f(72)等于——A p+q B 3p+2q C 2p+3q D p³+q³ 答案是什么不重要 我要解题过程或解题思路
f﹙72﹚=f﹙2×2×2×3×3﹚=f﹙2﹚+f﹙2﹚+f﹙2﹚+f﹙3﹚+f﹙3﹚=3p+2q
72=2*2*2*3*3
f(72)=f(8)+f(9) f(9)=f(3)+f(6)
f(8)=f(2)+f(4) f(6)=f(3)+f(3)
f(4)=f(2)+f(2)
f(6)=f(2)+f(3)=p+q
f(36)=2f(6)=2(p+q)
f(72)=f(36)+f(2)=2(p+q)+p=3p+2q
f(72)=f(8)+f(9)=3p+2q
f(8)=f(2)+f(4)=f(2)+f(2)+f(2)=3p
f(9)=f(3)+f(3)=2q
f(36)=2f(6)=2(f(2)+f(3))=2p+2q
f(72)=f(2)+f(36)=3q+2p
f(72)=f(8*9)=f(8)+f(9)
f(8)=f(2*4)=f(2)+f(4)=f(2)+f(2)+f(2)=3p
f(9)=f(3)+f(3)=2q
所以f(72)=3p+2q
解,由已知条件可得
f(72)=f(8×9)=f(8)+f(9)
=[f(2)+f(4)]+[f(3)+f(3)]
=[f(2)+f(2)+f(2)]+[f(3)+f(3)]
=3p+2q
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