第1个回答 2009-07-17
1
2*4^x=2*2^(2x)=2^(2x+1);
则2x+1=log2 16 =log2 2^4 =4;
则x=3/2
2
左:4^(3x+2)=2^(6x+4);
右:256*8^(1-x) = 2^8 * 2^(3-3x) =2^(11-3x)
则: 6x+4 =11-2x;
解得:x=7/9
3
2x^(3/4)-1=15
→2x^(3/4)=16;
→x^(3/4)=8;
→x=8^(4/3)=(8开立方)^4=2^4
=16;
4
2^(x+2)-6*2^(x-1)-8
= 4*2^x -6*2^x/2 -8
= 4*2^x -3*2^x-8
= 2^x-8;
则原方程即 2^x-8=0;
2^x=8=2^3
解得:x=3.
第2个回答 2009-07-17
(1)2*4^x=16
4^x=8
(2^2)^x=2^3
2^(2x)=2^3
2x=3
x=3/2
(2)4^(3x+2)=256*8^(1-x)
(2^2)^(3x+2)=(2^8)*(2^3)^(1-x)
2^(6x+4)=(2^8)*[2^(3-3x)]
2^(6x+4)=2^(11-3x)
6x+4=11-3x
9x=7
x=7/9
(3)2x^(3/4)-1=15
2x^(3/4)=16
x^(3/4)=8
两边四次方 x^3=8^4
x^3=(2^3)^4
x^3=(2^4)^3
x=2^4
x=16
(4)2^(x+2)-6*2^(x-1)-8=0
2^2*2^x-3*2*2^(x-1)-8=0
4*2^x-3*2^x-8=0
2^x-8=0
2^x=2^3
x=3
第3个回答 2009-07-17
(1)x=3/2
(2)x=7/9
(3)题目看不懂?
(4)x=3