Question

Log(2)1/25•log(3)1/8•log(5)1/9化简 还有已知log(18)9=

Log(2)1/25•log(3)1/8•log(5)1/9化简 还有已知log(18)9=a,log(18)5=b求log(36)45 值
在线等 有人吗

Answer 1

Log(2)1/25•log(3)1/8•log(5)1/9=(lg1/25/lg2)(lg1/8/lg3)(lg1/9/lg5)
=(lg1/25/lg5)(lg1/8/lg2)(lg1/9/lg3)=(-2)(-3)(-2)=-12

log(18)9=a,log(9)18=1/a=log(9)9+log(9)2=1+log(9)2,log(9)2=1/a-1=(1-a)/a
log(18)9/log(18)5=log(5)9=a/b
,log(18)5=b,log(5)18=1/b=log(5)9+log(5)2=a/b+log(5)2,log(5)2=1/b-a/b=(1-a)/b
log(18)9+log(18)5=log(18)45=a+b
log(45)2=lg2/(lg5+lg9)=1/[log(2)5+log(2)9]=1/[b/(1-a)+a/(1-a)]=(1-a)/(a+b)
log(36)45=lg45/lg18+lg2=1/[log(45)18+log(45)2]=1/[1/(a+b)+(1-a)/(a+b)]=(a+b)/(2-a)