Question

㏒14 7=a,㏒14 5=b,用a,b表示㏒35 28

过程详细点！

Answer 1

log 14 7 = lg 7 / lg 14
log 14 5 = lg 5 / lg 14

A = lg 7 / lg 14 = lg 7 / (lg 7 + lg 2)
B = lg 5 / lg 14 = (1 - lg2) / (lg 7 + lg 2)
通过以上两式可得:
lg 7 = A / (1 - A + B)
lg 2 = (1 - A) / (1 - A + B)
log 35 28
= lg 28 / lg 35
= (lg 7 + 2lg 2) / (lg 7 + lg 5)
= (lg 7 + 2lg 2) / (lg 7 + 1 - lg2)
= [A / (1 - A + B) + 2(1 - A) / (1 - A + B)] / [A / (1 - A + B) + 1 - (1 - A) / (1 - A + B)]
= [(2 - A) / (1 - A + B)] / [(A + B) / (1 - A + B)]
= (2 - A) / (A + B)

Answer 2

解：㏒35 28
=㏒35 2+log35 14
=㏒35 2+1/log14 5*7
=log35 2+1/(log14 5+㏒14 7)
=1/(a+b)+log35 2