Question

已知函數(shù)f(x)=log

1

3

x，若f（a³）+f（b³）=6，則f（ab）的值等于

2

．

Answer 1

分析：由題意，可先對(duì)方程f（a³）+f（b³）=6利用對(duì)數(shù)的去處性質(zhì)進(jìn)行化簡(jiǎn)，即可解出f（ab）=log

1

3

(ab)=2

解答：解：由題，函數(shù)f(x)=log

1

3

x，若f（a³）+f（b³）=6
∴log

1

3

a3+log

1

3

b3=6
∴3(log

1

3

a+log

1

3

b)=6
∴log

1

3

a+log

1

3

b=log

1

3

(ba)=2
∴f（ab）=log

1

3

(ab)=2
故答案為2

點(diǎn)評(píng)：本題考查對(duì)數(shù)的運(yùn)算性質(zhì)，熟練掌握對(duì)數(shù)的運(yùn)算性質(zhì)是解題的關(guān)鍵