Question

（1）log4 27乘以log25 8乘以log9 5 （2）（log4 3+log8 3）（log3 2+log9 2

Answer 1

⑴利用换底公式,将所有的式子换成以10为底的对数：
原式=lg27/lg4 × lg8/lg25 × lg5/lg9
=lg3³/lg2² × lg2³/lg5² × lg5/lg3²
=(3lg3)/(2lg2) × (3lg2)/(2lg5) × (lg5/2lg3)
=9/8
⑵由log(a^m) (b^n)=(n/m)loga b
则原式=(log2² 3 + log2³ 3)(log3 2 + log3² 2)
=[(1/2)log2 3 + (1/3)log2 3][log3 2 + (1/2)log3 2]
=[(5/6)log2 3][(3/2)log3 2]
=5/4