請教中四數學問題,勁人請入,急.......

[匿名]

2009-09-28 9:14 pm

1若(10^(1/3))^y=2,試不用計算y的值,求下列各式的值。
a)32/(10^2y)
b)100^(-y)

2a)計算起來((7+√45)^(1/2)-(7-√45)^(1/2))^2
b)由此計算,log((7+√45)^(1/2)-(7-√45)^(1/2))的值

更新1:

3.若log3=a及log5=b，以a及b表示log√50

回答 (1)

用戶10012

2009-09-28 9:45 pm

✔ 最佳答案

1. (10^(1/3))^y = 2
10^(y/3)= 2
10^(y/3)^3 = 2^3 = 8
so 10^y = 8.
a) 10^2y = (10^y)^2 = 8^2 = 64, so 32/(10^2y) = 32/64 = 1/2.
b) 100^(-y) = ((10^2)^(-y)) = 10^(-2y) = (10^y)^(-2) = 8^(-2) = 1/8^2 = 1/64.
2.
The expression = y = (7 + sqrt 45) + (7 - sqrt 45) - 2 sqrt(7 + sqrt45)sqrt(7 - sqrt 45) = 14 - 2 sqrt [ 7^2 - (sqrt 45)^2] = 14 - 2 sqrt ( 49 - 45) = 14 - 2 sqrt 4 = 14 - 4 = 10.
b) log [y^(1/4)] = 1/4 log y = 1/4 log 10 = 1/4.
3.
log sqrt 50 = log (50)^(1/2) = (1/2) log 50 = (1/2) log (5 x 10)
= (1/2) [ log 5 + log 10] = (1/2) [ b + 1].

👍 0 👎 0