一道高二数学题:比较log1/2(1/3)和log4 (8)的大小. 这个怎么比较?谢啦!
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一道高二数学题:比较log1/2(1/3)和log4 (8)的大小. 这个怎么比较?谢啦!
一道高二数学题:比较log1/2(1/3)和log4 (8)的大小. 这个怎么比较?谢啦!
一道高二数学题:比较log1/2(1/3)和log4 (8)的大小. 这个怎么比较?谢啦!
log1/2(1/3)=log2(3),
log4 (8)=log2²(8)=(1/2)log2(8)=log2(√8)=log2(2√2)
∵3>2√2,y=log2(x)是增函数
∴log1/2(1/3)>log4 (8).
log1/2(1/3)=log2(3)=log4 (9)
log4 (8)=3/2=1.5
4>1
log4 (x)在定义域R+为递增函数
9>8
∴log1/2(1/3)>log4 (8)
ps(1)log(a)(MN)=log(a)(M)+log(a)(N);
2)log(a)(M/N)=log(a)(M)-log(a)(N); ...
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log1/2(1/3)=log2(3)=log4 (9)
log4 (8)=3/2=1.5
4>1
log4 (x)在定义域R+为递增函数
9>8
∴log1/2(1/3)>log4 (8)
ps(1)log(a)(MN)=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) (n∈R)
(4)log(a^n)(M)=(1/n)log(a)(M)(n∈R)
5)log(A)M=log(b)M/log(b)A (b>0且b≠1)
(6)a^(log(b)n)=n^(log(b)a)
(7)对数恒等式:a^log(a)N=N;
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