log a 2+log a 2分之1

来源：学生作业帮编辑：作业帮分类：数学作业时间：2024/11/05 15:18:01

log a 2+log a 2分之1
log3 18-log3 2
2log5 25-3log2 64
已知lg2=a lg3=b求下列各式的值
1.lg6 2.log3 4 3.log2 12 4.lg2分之3
已知X的对数,求X
1.lgx=lga+lgb 2.loga x=loga m-loga n
3.lgx=31gn-lgm 4.loga x=2分之1loga b-loga c
呵呵不好意思最后问一题
2log5 10+log5 0.25

log a 2+log a 1/2
=loga (2×1/2)
=loga 1
=0
log3 18-log3 2
=log3 (18÷2)
=log3 9
=log3 3^2
=2log3 3
=2
2log5 25-3log2 64
=2lg25/lg5-3lg64/lg2
=2lg5^2/lg5-3lg2^6/lg2
=2×2lg5/lg5-3×6lg2/lg2
=4-18
=-14
已知lg2=a lg3=b求下列各式的值
1.lg6=lg(2×3)=lg2+lg3=a+b
2.log3 4=lg4÷lg3=lg2^2÷lg3=2lg2÷lg3=2a/b
3.log2 12=lg12÷lg2=lg(2^2×3)/a=(lg2^2+lg3)/a=(2lg2+b)/a=(2a+b)/a
4.lg2分之3=lg(3÷2)=lg3-lg2=b-a
已知X的对数,求X
1.lgx=lga+lgb=lg(a×b)=lg(ab)
x=ab
2.loga x=loga m-loga n=loga (m÷n)=loga m/n
x=m/n
3.lgx=31gn-lgm=lgn^3-lgm=lg(n^3÷m)=lg(n^3/m)
x=n^3/m
4.loga x=2分之1loga b-loga c=loga b^(1/2)-loga c=loga [b^(1/2)÷c]
x=b^(1/2)÷c=(√b)/c
2log5 10+log5 0.25
=log5 10^2+log5 0.25
=log5 (10^2×0.25)
=log5 25
=log5 5^2
=2log5 5
=2

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