已知a大于b大于1,log(a)b+log(b)a=10/3,求log(a)b-log(b)a的值
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已知a大于b大于1,log(a)b+log(b)a=10/3,求log(a)b-log(b)a的值
谢谢你的回答,但是log(a)b*log(b)a=1 是怎么出来的呢?
谢谢你的回答,但是log(a)b*log(b)a=1 是怎么出来的呢?
因为log(a)b*log(b)a=1
[log(a)b+log(b)a]^2-[log(a)b-log(b)a]^2=4log(a)b*log(b)a=4
可以解得log(a)b-log(b)a=8/3 或者为- 8/3
因为a>b>1
则log(a)b< log(b)a ,log(a)b-log(b)a为负数
所以log(a)b-log(b)a=-8/3
把log(a)b 可以化为log(10)b/log(10)a
所以log(a)b*log(b)a=log(10)b/log(10)a
乘以log(10)a/log(10)b=1
[log(a)b+log(b)a]^2-[log(a)b-log(b)a]^2=4log(a)b*log(b)a=4
可以解得log(a)b-log(b)a=8/3 或者为- 8/3
因为a>b>1
则log(a)b< log(b)a ,log(a)b-log(b)a为负数
所以log(a)b-log(b)a=-8/3
把log(a)b 可以化为log(10)b/log(10)a
所以log(a)b*log(b)a=log(10)b/log(10)a
乘以log(10)a/log(10)b=1
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