Question

已知m、n满足25^m*2*10^n=5^7*2^4,求√(m^2+n^2)的值

Answer 1

25^m*2*10^n=5^7*2^4

5^2m*2^(n+1)*5^n=5^7*2^4

2m+n=7

n+1=4

m=2

n=3

将m,n分别代入即可求得√(m^2+n^2)的值