已知log18(3)=a,18^b=5,试用a,b表示log36(45)=_数学解答

已知log18(3)=a,18^b=5,试用a,b表示log36(45)=

人气：273 ℃　时间：2020-05-11 03:28:17

解答

a=log18(3)
b=log18(5)
log36(45)=log18(45)/log18(36)=log18(3X3X5)/log18(18X2)=[2log18(3)+log18(5)]/[1+log18(2)]=(2a+b)/[1+log18(18/9)]=(2a+b)/[1+1-log18(9)]=(2a+b)/(2-2log18(3))=(2a+b)/(2-2a)