Question

已知log14 7=a,log14 5=b,用a,b表示log35 28

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)