maths

1.4^(x-1)=320-4^x
4^(x-1)+4^x=320
4^(x-1)(1+4)=320
4^(x-1)=64
4^(x-1)=4^3
x-1=3
x=4

2.2^(x+2)-6*2^(x-1)-8=0
2^(x+1)-3*2^(x-1)-4=0
4*2^(x-1)-3*2^(x-1)-4=0
2^(x-1)=4
2^(x-1)=2^2
x-1=2
x=3

3.(x+m^2)^3=-n^2---(1)
m=n^(1/3)---(2)
From (2)
n=m^3
n^2=m^6
-n^2=-m^6---(3)
Sub (3) in (1)
(x+m^2)^3=-m^6
x+m^2=-m^2
x=-2m^2---(4)
Sub (2) in (4)
x=-2(n^1/3)^2
=-2n^(2/3)

1)
4^(x-1) = 320 - 4^x
(4^x)(4^-1) = 320 - 4^x
(4^x)/4 + 4^x = 320
(4^x)*(1/4 + 1) = 320
4^x = 320/(1.25)
4^x = 256
4^x = 4^4

therefore x = 4

2)
2^(x+2) - 6*2^(x-1) - 8 = 0
(2^x)*2^2 - 6*(2^x)*(2^-1) - 8 = 0
(2^x)[4 - 6*(1/2)] = 8
2^x = 8/1
2^x = 8
2^x = 2^3

therefore
x = 3

3)
sub m=n^(1/3) into (x+m^2)^3=-n^2

{x + [n^(1/3)]^2}^3 = -n^2
x + n^(1/3*2) = -n^(2*1/3)
x + n^(2/3) = -n^(2/3)
x = -n^(2/3) - n^(2/3)
x = -2n^(2/3)

m = n^(1/3)
n = m^3 into (x+m^2)^3=-n^2
(x + m^2)3 = -(m^3)^2
x + m^2 = -(m^6)^(1/3)
x + m^2 = -m^2
x = -m^2 - m^2
x = -2m^2

As follows~~~


圖片參考：http://i182.photobucket.com/albums/x4/A_Hepburn_1990/mathslog2.jpg?t=1186127109