Question

高一数学对数运算题目

Answer 1

ln7/ln14 = a , so ln7 = a*(ln7+ln2), so (1-a)*(ln7) = a*(ln2), so ln2 = (1/a -1)*(ln7)
ln5/ln14 = b, so ln5 = b*(ln7 +ln2),

ln 28/ln35 = (ln4 + ln7) / (ln5 + ln7)
= (2ln2 + ln7) / (ln5 + ln7)
= (2ln2 + ln7)/[b*(ln7+ln2) + ln7]
= [2*(1/a-1)*(ln7) + ln7] / [ b*(ln7)/a + ln7]
= (2/a -1)/(b/a + 1)
= (2-a)/(b+a),

Answer 2

28=14^2/7,
换底得log<35>28=log<14>28/log<14>35
=(2-log<14>7)/(log<14>7+log<14>5)
=(2-a)/(a+b).

Answer 3

log14(7)+log14(5)=log14(7x5)=a+b
log14(35)=a+b
log35(14)=1/(a+b)
log14(7)/log14(5)=log5(7)=a/b
log5(7)=log5(2+5)=log5(2)+1=a/b
log5(2)=a/b-1
log14(2)=log5(2)log14(5)=a-b
log35(2)=log14(2)log35(14)=(a-b)/(a+b)
log35(28)
=log35(14x2)
=log35(14)+log35(2)
=(a-b)/(a+b)+1/(a+b)
=(a-b+1)/(a+b)

Answer 4

把它换成底数为14来算不就好了吗。

Answer 5

你用换底公式吧