设18^b=5,18^a=9,试用a、b表示log(72)45.

18^a=9
a=log(18)9
=ln9/ln18
=ln9/(ln2+ln9)
1/a=(ln2+ln9)/ln9=ln2/ln9+1
ln2/ln9=1/a-1
即ln2=ln9*(1/a-1)

18^b=5
b=log(18)5
=ln5/ln18
a=ln9/ln18
a/b=ln9/ln5
ln5=ln9*b/a

log(72)45
=ln45/ln72
=(ln5+ln9)/(3ln2+ln9)
=(ln9*b/a+ln9)/[3*ln9*(1/a-1)+ln9]
=[(a+b)/a]/[(3/a-3)+1]
=(a+b)/(3-2a)

18^b=5,18^a=9,所以18^b*18^a=5*9=45,即18^(a+b)=45
log(72)45=x,则72^x=45
所以72^x=18^(a+b)，则x=log(72)18^(a+b)=(a+b)log(72)18