Question

设2^a=5^b=m,且1/a+1/b=2,则m=? 要详细步骤

Answer 1

已知2^a=5^b=m

∴m∈R＋

∴a=㏒�6�0m b=㏒5 m(同前面那种写法)

又∵1/a+1/b=2且m∈R＋

∴1/㏒�6�0m+㏒5 m=2

由换底公式可得 ㏒m 2+㏒m 5=2 即 ㏒m 10=2

∴㏒m 10=㏒m m�0�5 即 m�0�5=10

∴m=�0�5√10=10^(1/2)

Answer 2

a＝log2 m,b＝log5 m.
1／log2 m＋1／log5 m＝2
logm 2＋logm 5＝2
logm 10＝2
m＝根号10

Answer 3

a=log(2,m) b=log(5,m)1/a+1/b=log(m,2)+log(m,5)=log(m,10)=2 即m�0�5=10 m=根号10