Logarithm question

足球博士 is WRONG. Because (log a) ^ 2 ≠ loga^2
Answer:
(log a) ^ 2 - log a ^ 5 + 6 = 0
(log a) ^ 2 - 5 log a + 6 = 0
Let x be log a
x^2 - 5 x + 6 = 0
(x-3)(x-2) = 0
x = 3 or x = 2
∴ log a = 3 or log a = 2
a = 10^3 or a= 10^ 2
a = 1000 or a = 100

2006-10-28 19:59:12 補充：
beckyip127 is also WRONG.Because X^2 - 5X 6 ≠ ( X - 6 )( X 1) 6 唔能夠拆成 ㄧ6同 1But 能夠拆成 ㄧ3 同 ㄧ2

2006-10-28 20:04:47 補充：
log a ^ n ≠ (log a)^n log a ^n = n log a....................................If log x = y x = 10 ^ y Because the 冇寫base 就當base 係 10 ~希望幫到你而你又真係明la　!！

2006-10-29 20:47:00 補充：
紙皮B
Answer is WRONG.Because (log a)(log a) - (5)(log a) + 6 = 0Then,let y=log a,∴y^ 2 -y+6=0 is WRONG y^2 - 5 y + 6 = 0 is CORRECT.

∵(log a) ^ 2 - log a ^ 5 + 6 = 0

∴(log a)(log a) - (5)(log a) + 6 = 0

Then,let y=log a,

∴y^ 2 -y+6=0

However,∵Δ(i.e.b^2-4ac)<0,∴there are no real solutions.

*If the qustion is (log a) ^ 2 - log a ^ 5 - 6 = 0,it can be calculated.

Solution:

Let y =log a,

∴ y^2 - y - 6 = 0

(y - 3)(y + 2) = 0


∴ y = 3 or y = -2

(log a) ^ 2 - log a ^ 5 + 6 = 0
(log a) ^ 2 - 5 * log a + 6 = 0
(log a - 3) (log a - 2) = 0

log a = 3 or log a = 2
a = 1000 or a = 100

Note: log (a^n) = n log a
but (log a) ^ n is not equal to (n log a)

let X be (log a)
X^2 - 5X + 6 = 0
( X - 6 )( X + 1)=0
X=6 or X= -1(rej) (* log a > 0)
so
log a =6
a= 1000000

2006-10-28 19:55:17 補充：
(*log a must be bigger than or equal to 0)

2006-10-28 19:57:35 補充：
Oh ... I am sorry that I read the question carelessly..MoDeL AnSweR!'s answer should be correct then..