设log以8为底的9的对数=a,log以3为底的5的对数,则lg2=_数学解答

设log以8为底的9的对数=a,log以3为底的5的对数,则lg2=

人气：300 ℃　时间：2020-01-26 07:14:13

解答

LOG(8,9)=ALOG(3,5)=BA=LG(9)/LG(8)=2LG(3)/(3LG(2)) ==>LG(3)=A/(6LG(2))B=LG(5)/LG(3)=(1-LG(2))/LG(3)==> LG(3)=(1-LG(2))/B设LG(2)=X则有 A/(6X)=(1-X)/BAB=6X-X^2X^2-6X+AB=0则有X1 =(6+(36-4AB)^(1/2))/2=3+(9...