Question

log14,7=a,log14,5=b,则用a,b表示log35,28=?

Answer 1

log14,7=a,log14,5=b,则用a,b表示log35,28
log14,35=a+b
log35,14=-(a+b)
log14,7=log2*7,7=-(log7,2*7)=-(log7,7+log7,2)=-1-log7,2=a
∴log7,2=1-a
log14,5=log2*7,5=-(log2,5+log7,5)=b 得
-b=log2,5+log7,5=log2,5+log2,5/log2,7
∴有log2,5/(a-1)+log2,5=-b 计算得log2,5=-b(a-1)/a
log35,28
=log35,14*2=log35,14+log35,2
=-(a+b)+log35,2
=-(a+b)-log2,5-log2,7
=-(a+b)-(-b(a-1)/a)+(1-a)
=-2a+1-(b/a)