Question

log【2】(log【8】m) =log【8】（log【2】m），求（log【2】m）的平方 【】内为底

Answer 1

8=2^3，所以log【8】m=三分之一log【2】m
设log【2】m=x
所以log【2】(三分之一x）=三分之一log【2】x，所以三分之一x=x^3,因为x>0，
所以三分之一=x^2，所以（log【2】m）的平方=1/3

追问

标准答案是27，我想知道过程，不知道您能再思考一下否？多谢

追答

哦，对我错了
设log【2】m=x
所以log【2】(三分之一x）=三分之一log【2】x，所以三分之一x=x的三分之一次方，
两边约去三次根号x，所以三次根号x^2=3，两边三次方得x^2=27，所以（log【2】m）的平方=27
看看懂了么

Answer 2

已知:log2|(log8|m)=log8|(log2|m)，求(log2|m)².
解:log2|(log2³|m)=log2³|(log2|m)
log2|((1/3)×log2|m)=log2|(log2|m)^(1/3)
(1/3)×log2|m=(log2|m)^(1/3)
则log2|m=3^(3/2)
则(log2|m)²=(3^(3/2))²=3³=27

追问

^是啥意思啊？谢谢

追答

a^b是a的b次方的意思，
loga|b当然就是以a为底，b的对数了！

Answer 3

log【2】(log【2】m^1/3) =log【2】（log【2】m）^1/3
log【2】m^1/3=（log【2】m）^1/3
1/3*log【2】m=（log【2】m）^1/3
1/3*(log【2】m)^2/3=1
(log【2】m)^2=3^3=27
（log【2】m）的平方=27

追问

符号 ^ 是啥意思啊？谢谢

追答

^表示几次方，^2平方

Answer 4

8^[log【2】(log【8】m)]=8^[log【8】（log【2】m）]
(log【8】m)^3=log【2】m
8^(log【8】m)^3=8^[log【2】m]
8^[log【8】m*[log【8】m]^2]]=2^[3*log【2】m]
m^[log【8】m]^2]=m^3
[log【8】m]^2=3
又log【8】m=1/3log【2】m
[log【8】m]^2=1/9[log【2】m]^2=3
[log【2】m]^2=27
我的答案应该没问题，有疑惑请追问

Answer 5

1

追问

答案是27,要过程