Question

log2 3=a,log3 7=b,用a,b表示log14 56

log2 3=a表示a是以2为底3的对数

Answer 1

利用换底公式即可.
log42^56=(log2^56)/(log2^42)
=[log2^(8*7)]/[log2^(2*3*7)]
=[3+log2^7]/[1+log2^3+log2^7]
而log2^7=(log3^7)/(log3^2)=b/a
其中log3^2=1/(log2^3)
代入即可.

Answer 2

会几个概念就很简单了。
1.loga b=1/logb a.
2.lg(ab)=lga+lgb;
3.loga b=lgb/lga.

把这几个应用进去，得log14 56=ab/(1+ab)+3ab+3.

Answer 3

a=lg3/lg2
lg2=lg3/a

b=lg7/lg3
lg7=blg3

log14 56=lg56/lg14=(lg7+lg8)/(lg7+lg2)=(lg7+3lg2)/(lg7+lg2)
=(blg3+3lg3/a)/(blg3+lg3/a)
=(b+3/a)/(b+1/a)
=(ab+3)/(ab+1)

Answer 4

log14 56=log3 56/log3 14=log3 7*8/log3 7*2=(log3 7+3log3 2)/(log3 7+log3 2)=(b+3/a)/(b+1/a)

Answer 5

ln3/ln2=a
ln7/ln3=b
ln7/ln2=ab
ln56/ln14=(ln7+3ln2)/(ln2+ln7)=(ab+3)/(1+ab)