F.4 Certificate Maths!!!急問~~~Logarithmic Equations...*= ]

1.
9^x - 10(3^x) + 9 =0
3^2x - 10(3^x) + 9 = 0
Let 3^x = X (This make you to see the equation easier)
X^2 - 10X + 9 = 0
(X - 1)(X - 9) = 0
X = 1 or 9
Therefore, 3^x = 1 or 9
i.e. x = 0 or 2

2.
2^(2x) - 7(2^x)-8 =0
Let 2^x = X
X^2 - 7X - 8 = 0
(X + 1)(X - 8) = 0
X = -1 or 8
Since 2^x will never be -1, 2^x = 8
x = 3

3.
4^x - 6(2^x) + 8 =0
2^2x - 6(2^x) + 8 = 0
Let 2^x = X
X^2 - 6X + 8 = 0
(X - 2)(X - 4) = 0
X = 2 or 4
Therefore 2^x = 2 or 4
i.e. x = 1 or 2

4.
4^(x+1) - 2^(x+2) + 1=0
2^[2(x + 1)] - 2* 2^(x + 1) + 1 = 0
Let 2^(x + 1) = X
X^2 - 2X + 1 = 0
(X - 1)^2 = 0
X = 1
Therefore, 2^(x + 1) = 1
x + 1 = 0
x = -1