Question

log以三为底2的对数和log以5为底2的对数，怎么比较大小

Answer 1

取倒数比较

0<log2底3<log2底5

0<1/log3底2<1/log5底2

log3底2>log5底2

根据换底公式：log2为底9的对数=log3为底9的对数除以log3为底2的对数log3为底2的对数=log3为底2的对数除以log3为底3的对数两者相乘，约分后得

log3为底9的对数除以log3为底3的对数=3

扩展资料

对数的运算法则：

1、log(a) (M·N）=log(a) M+log(a) N

2、log(a) (M÷N)=log(a) M-log(a) N

3、log(a) M^n=nlog(a) M

4、log(a)b*log(b)a=1

5、log(a) b=log (c) b÷log (c) a

Answer 2

取倒数比较
0<log2底3<log2底5
0<1/log3底2<1/log5底2
log3底2>log5底2