數學題(log)

log8(X - 5) = 2/3
82/3 = X - 5
4 = X - 5
X = 9
log(X + 3) + log(X + 12) - 1 = 0 ; X > -12
log(X + 3) + log(X + 12) = 1
log(X + 3)(X + 12) = 1
(X + 3)(X + 12) = 10
X2 + 15X + 36 = 10
X2 + 15X + 26 = 0
(X + 13)(X + 2) = 0
X = -13(rejected) or X = -2
(logX)2 - logX2 = 3
(logX)2 - 2logX - 3 = 0
Let logX = u; X>0
u2 - 2u - 3 = 0
(u - 3)(u + 1) = 0
u = 3 or u = -1(rejected)
logX = 3
X = 103 = 1000

2009-09-14 19:03:38 補充：
Correction: -1 is not rejected
logX = -1
X = 10^-1 = 0.1

2009-09-14 19:06:23 補充：
Just too quick

2009-09-14 19:37:50 補充：
log(a)b = x <=> b^x = a這是定義,要記. 如10^4 = 10000, log10000 =4
5^3 = 125, log(5)125 = 3

logX = Y => 10^Y = X, X一定是正數.

For Q 3, why u can't be -1?
when u = -1, X = 0.1, still positive