对数函数比较大小 用到等差数列的知识好像a>b>c>d>0,a、b、c、d成等差数列,比较log10(a比b),log10(b比c),log10(c比d).
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![对数函数比较大小 用到等差数列的知识好像a>b>c>d>0,a、b、c、d成等差数列,比较log10(a比b),log10(b比c),log10(c比d).](/uploads/image/z/14834051-35-1.jpg?t=%E5%AF%B9%E6%95%B0%E5%87%BD%E6%95%B0%E6%AF%94%E8%BE%83%E5%A4%A7%E5%B0%8F+%E7%94%A8%E5%88%B0%E7%AD%89%E5%B7%AE%E6%95%B0%E5%88%97%E7%9A%84%E7%9F%A5%E8%AF%86%E5%A5%BD%E5%83%8Fa%EF%BC%9Eb%EF%BC%9Ec%EF%BC%9Ed%EF%BC%9E0%2Ca%E3%80%81b%E3%80%81c%E3%80%81d%E6%88%90%E7%AD%89%E5%B7%AE%E6%95%B0%E5%88%97%2C%E6%AF%94%E8%BE%83log10%EF%BC%88a%E6%AF%94b%EF%BC%89%2Clog10%EF%BC%88b%E6%AF%94c%EF%BC%89%2Clog10%EF%BC%88c%E6%AF%94d%EF%BC%89.)
对数函数比较大小 用到等差数列的知识好像a>b>c>d>0,a、b、c、d成等差数列,比较log10(a比b),log10(b比c),log10(c比d).
对数函数比较大小 用到等差数列的知识好像
a>b>c>d>0,a、b、c、d成等差数列,比较log10(a比b),log10(b比c),log10(c比d).
对数函数比较大小 用到等差数列的知识好像a>b>c>d>0,a、b、c、d成等差数列,比较log10(a比b),log10(b比c),log10(c比d).
设公差为q,就有q=a-b>0;
a/b=(b+q)/b=1+q/b;
b/c=(c+q)/c=1+q/c;
c/d=(d+q)/d=1+q/d;
由于 b>c>d,有 a/b
解法一:赋值法:令d=10,c=20,b=30,a=40
则log10(a比b)=lg0.75 log10(b比c)=lg1.5 log10(c比d)=lg2
结果一目了然:log10(a比b)
log10(a比b)- log10(b比c)=lg(ac/b^2)=lg...
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解法一:赋值法:令d=10,c=20,b=30,a=40
则log10(a比b)=lg0.75 log10(b比c)=lg1.5 log10(c比d)=lg2
结果一目了然:log10(a比b)
log10(a比b)- log10(b比c)=lg(ac/b^2)=lg[(b+q)*(b-q)/b^2]=lg[(b^2-q^2)/b^2]<0
因为b^2-q^2所以log10(a比b)< log10(b比c)
同理可得log10(b比c)< log10(c比d)
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