设log以8为底的9的对数=a,log以3为底的5的对数,则lg2=
问题描述：
设log以8为底的9的对数=a,log以3为底的5的对数,则lg2=
答
log8 9=a,log8 3=a/2,log2 3=3a/2
log3 5=log2 5/log2 3=b
log2 5=log3 5×log2 3=3ab/2
log2 5=lg5/lg2=(1-lg2)/lg2=3ab/2
3ab×lg2=2(1-lg2)
3ab×lg2=2-2lg2
(3ab+2)lg2=2
lg2=(3ab+2)/2=1+3ab/2
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...