F.4 MATHSS LOG

用戶191146

2012-12-13 3:01 am

1. log (base a) 18= 2, then a = ??

2. log(base3) {log(base 2) x} = a, then x =??

3. If 3^a = 2, then log(base 3) 2/3 = ??

4. log ( x^3 - y^3)=??

5. a^2 - b^2 /{ a^(-2) - b^(-2)} = ??

6. If 3^(x-1) = 2 , 3^(-2x) = ??

7. (3^3n x 2^2n) / 12^n = ??

8. If 27^k = a , then 9^k =?

9. a^(m-n) / b^n = ??

回答 (1)

50418129

2012-12-13 6:37 pm

✔ 最佳答案

(1)　a^2 = 18 => a = sqrt(18) = 3sqrt(2)
(2)　log(base 2) x = 3^a => x = 2^(3^a)
(3)　a = log(base 3)2
　　log(base 3) 2/3 = log(base 3) 2 - log(base 3) 3 = a - 1
(4)　log (x - y)(x^2 + xy + y^2) = log (x - y) + log(x^2 + xy + y^2)
(5)　(a^2 - b^2) / [(b^2 - a^2) / (ab)^2] = -(ab)^2
(6)　3^x / 3^1 = 2 => 3^x = 6 => 3^(2x) = 6^2 = 36 => 3^(-2x) = 1/36
(7)　27^n x 4^n / 12^n = 9^n
(8)　3^(3k) = a => 3^(k) = a^(1/3) => 3^(2k) = a^(2/3)
(9)　a^m / (a^n)(b^n) = a^m / (ab)^n

參考: knowledge

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