急,几道有关对数的题,要详~看质量再重赏

急,几道有关对数的题,要详~看质量再重赏
1.log(√2)4+log(4)8+{(1/6)＾[log(6)1/5]}
（√2即根号2）
2.log(2)125•log(3)16•log(5)27
3.已知(3＾a)=(4＾b)=A,且（1/a）+(1/b)=2,求A的值
4.已知log（2）3=a,3＾b=5,用a、b表示log(18)45
5.若x•log(5)4=2,求（4＾x）+(4＾-x)及(16＾x)+(16＾-x)的值

1.log(√2)4+log(4)8+{(1/6)＾[log(6)1/5]}
=log[2^(1/2)](2^2)+log(2^2)(2^3)+{(1/6)＾{log[(1/6)^(-1)]5^(-1)]}
=log[2^(1/2)](2^2)+log(2^2)(2^3)+{(1/6)＾[log(1/6)5]}
=4+1.5+5
=11.5
2.2.log(2)125•log(3)16•log(5)27
=lg125/lg2•lg16/lg3•lg27/lg5
=(3lg5•4lg2•3lg3)/(lg5•lg2•lg3)
=3•4•3
=36
3.已知 (3 ＾a) = (4 ＾b) = A,且 (1/a) + (1/b) = 2,求A的值
1/Log[3,A] + 1/Log[4,A] = 2,
Log[A,3] + Log[A,4] = 2,
Log[A,12] = 2,
A = √[12] = 2 √[3]
4.
已知log (2) 3 = a,3＾b = 5,用a、b表示log (18) 45
Log[2,3] = a,Log[3,5] = b,
所以Log[2,5] = a b
Log[18,45]
= Ln[45]/Ln[18]
= (Ln[5] + Ln[9])/(Ln[2] + Ln[9])
= (Ln[5] + 2 Ln[3])/(Ln[2] + 2 Ln[3])
= Ln[5]/(Ln[2] + 2 Ln[3]) + (2 Ln[3])/(Ln[2] + 2 Ln[3])
= 1/((Ln[2] + 2 Ln[3])/Ln[5]) + 1/((Ln[2] + 2 Ln[3])/(2 Ln[3]))
= 1/(Ln[2]/Ln[5] + (2 Ln[3])/Ln[5]) +
1/(Ln[2]/(2 Ln[3]) + (2 Ln[3])/(2 Ln[3]))
= 1/(1/(a b) + 2/b) + 1/(1/(2 a) + 1)
= (a (2 + b))/(1 + 2 a)
5
若xlog (5) 4 = 2,求 4 ^ x + (4 ＾ - x) 及 (16 ＾x) + (16 ＾ - x) 的值
Log[5,4] x = 2,
x = 2/Log[5,4] = 1/Log[5,2] = Log[2,5],
4 ＾x + 4 ＾ (-x) =
2^(2 Log[2,5]) + 2^(-2 Log[2,5]) = 5^2 + 5^-2 = 626/25,
4 ＾x + 4 ＾ (-x) = (2^x + 2^(-x))^2 -
2 = (2^Log[2,5] + 2^-Log[2,5])^2 - 2 = (5 + 1/5)^2 - 2 = 626/25,
16 ＾x + 16 ＾ (-x) = (4 ＾x + 4 ＾ (-x))^2 - 2 = (626/25)^2 - 2 =
(390626/ 625 )