2^a=5^b=m,且1/a+1/b=2,求m的值.m不等于0

2^a=5^b=m,且1/a+1/b=2,求m的值.m不等于0

2^a=5^b=m
a=log2(m) 1/a=logm(2)
b=log5(m) 1/b=logm(5)
1/a+1/b=2
logm(2)+logm(5)=2
logm(10)=2
m=√10