高手请进,几道指对方程~~
来源:百度知道 编辑:UC知道 时间:2024/06/23 18:46:53
(!)x^(lgx)=x^3/100
(2)f(x)=lg(ax+1)在(-无穷大,1)上有意义,a的取值范围
(3)(lg)^x-2lgx-2=0有两个根a,b,则loga(b)+logb(a)=____.
(4)若a>0,2^(3x)-2^x=a(2^x-2^(-x))的解
(5)5^(x-1)=3^(x^-1)
(6)log5(4^x+144)-4log5(2)=log[5(2^(x-2)+1)]
单独的^为平方.
谢!
要详细过程~~
(2)f(x)=lg(ax+1)在(-无穷大,1)上有意义,a的取值范围
(3)(lg)^x-2lgx-2=0有两个根a,b,则loga(b)+logb(a)=____.
(4)若a>0,2^(3x)-2^x=a(2^x-2^(-x))的解
(5)5^(x-1)=3^(x^-1)
(6)log5(4^x+144)-4log5(2)=log[5(2^(x-2)+1)]
单独的^为平方.
谢!
要详细过程~~
1.
x^(lgx)=x^3/100
10^((lgx)^2)=10^(3lgx - 2)
这里 x 应该是实数 ..
所以..
(lgx)^2 = 3lgx - 2
(lgx)^2 - 3lgx + 2 = 0
lgx1 = 1, lgx2 = 2
x1 = 10, x2 = 100
2.
由题意
x>=1 <=> ax+1<=0
-1/a >= 1
a <= -1
3.
loga(b)+logb(a)
= lgb/lga + lga/lgb
= ((lga+lgb)^2 - 2lgalgb) / lgalgb
= (2^2 - 2(-2)) / -2
= -4
4.
设 2^x = k
k^3 - k = a(k - 1/k)
k(k + 1)(k - 1) = a (k + 1)(k - 1) / k
显然, (k + 1) 不等于 0
所以 k^2 (k - 1) = a (k - 1)
(k^2 - a)(k - 1) = 0
因为 a > 0
所以
k1 = sqrt(a), k2 = -sqrt(a), k3 = 1
所以
x1 = log(2)sqrt(a), .. , x3 = 0
5.
5^(x-1)=3^(x^2-1)
lg5(x-1)=lg3(x-1)(x+1)
(x-1)(lg5-xlg3-lg3) = 0
x1 =