Question

已知log14 7=a,log14 5=b,求log35 28

Answer 1

log14 7+log14 5= log14 35=a+b

log35 14=1/(a+b)

又由换底公式,log14 7=log35 7 / log 35 14

log35 7=log14 7 * log35 14=a/(a+b)

所以log35 2=log35 (14/7)=log35 14 - log35 7 =1/(a+b) - a/(a+b)=(1-a)/(a+b)

log35 28=log35 14 +log35 2=(2-a)/(a+b)