已知11.2^m=100,0.112^n=100,则1/m-1/n的个数是1

Question

已知11.2^m=100,0.112^n=100,则1/m-1/n的个数是 1

Answer 1

11.2^m=100,m=log_11.2(100)=ln(100)/ln(11.2)
0.112^n=100,n=log_0.112(100)=ln(100)/ln(0.112)
1/m-1/n
=ln(11.2)/ln(100)-ln(0.112)/ln(100)
=[ln(11.2)-ln(0.112)]/ln(100)
=ln(11.2/0.112)/ln(100)
=ln(100)/ln(100)
=1