Question

已知,16^m=4X2^2m,27^n=9X3^n+2,求m,n的值

Answer 1

16^m=4*2^2m,

(2^4)^m=2^2*2^2m

2^4m=2^(2m+2)

4m=2m+2

2m=2

m=1

27^n=9*3^n+2,

(3^3)^n=3^2*3^n+2

3^3n=3^(n+4)

3n=n+4

2n=4

n=2