(1)假设x=log(a)N,N=a^x 假设y=log(m)N,N=m^y 假设z=log(m)a,a=m^z 那么N=a^x=m^y,a=m^z,代入 (m^z)^x=m^y,也就是m^(zx)=m^y,即zx=y 这样就有log(a)N=log(m)N/log(m)a (2)log(2)25=2log(2)5,log(3)4=2log(3)2,log(5)9=2log(5)3 log(2)25*log(3)4*log(5)9 =8log(2)5*log(3)2*log(5)3 log(2)5=log(3)5/log(3)2 原式=8log(3)5*log(5)3=8 (3)log(a)b=log(c)b/log(c)/a log(a)b*log(b)c*log(c)a=log(b)c*log(c)b=log(c)c/log(c)b*log(c)b=log(c)c=1 a