Question

高一数学必修一 74页 A组

3.计算:
(1) loga2+loga2分之1 (a>0,且a不等於1)
(3)log4分之1-lg25
4已知lg2=a,lg3=b,求下列各式的值:
(1) lg6 (4)lg2分之3

5.已知x的对数,求x
(1)lgx=lga+lgb
(4) logax=2分之1logab-logac

Answer 1

3.计算:
(1) loga2+loga2分之1 (a>0,且a不等於1)
=loga2+loga2^(-1)
=loga2-loga2
=0
(3)log4分之1-lg25
=lg(1/4)/25
=lg(1/100)
=lg10^(-2)
= -2lg10
= -2

4已知lg2=a,lg3=b,求下列各式的值:
(1)lg6
=lg(2*3)
=lg2+lg3
=a+b
(4)lg2分之3
=lg3-lg2
=b-a

5.已知x的对数,求x
(1)lgx=lga+lgb
lgx=lgab
x=ab
(4) logax=2分之1logab-logac
2logax=logab-2logac
logax^2=logab-logac^2
logax^2=loga(b/c^2)
x^2=b/c^2
x=1/c* √b
【这道题我怀疑你抄错题了，如果是 logax=2分之1(logab-logac)，则】
logax=2分之1(logab-logac)
2logax=2logab-2logac
logax^2=logab^2-logac^2
logax^2=loga(b^2/c^2)
x^2=b^2/c^2
x=b/c

Answer 2

4：(1):lg6=lg(2×3）＝lg2+lg3=a+b