✔ 最佳答案
1)
已知log 3=p 及 log 5=q,試以p和q表示:
log√243/2
= [ log (243/2)] / 2
=(log 243 - log 2) / 2
=[log 243 - log (10/5)] /2
=[log 243 - (log 10 - log 5)]/2
=(5 log 3 - 1 + log 5)/2
=(5p+q-1)/2
2)
解下列方程:
2^4x -5(2^2x+1)+24=0
2^4x -5(2^2x) * 5 +24=0
2^4x - 25(2^2x) + 24 = 0
2^2x = 24 or 2^2x = 1
2x = log 24 / log 2 or 2x = log 1 / log 2
x = log 24 / 2 log 2 or x = 0
3)
解下列聯立方程:
a.
{5^2x-y =625...........(1)
{log 10x+log4y =1....(2)
From (2),
log 10x + log 4y = log 10
log [(10x)(4y)] = log 10
40xy = 10
4xy = 1
x = 1/4y .........(3)
Substitute (3) into (1),
5^(1/2y - y) = 625
5^(1/2y - y) = 5^4
1/2y - y = 4
1 - 2y^2 = 8y
2y^2 + 8y - 1 = 0
y = (-8 + 6√2 )/4
=(-4 + 3√2) / 2
=0.121
x = 1/4y
= 1/ (-8 + 6√2)
=2.601
2006-12-13 19:45:49 補充：
2)解下列方程:2^4x -5(2^2x 1) 24=02^4x -5[(2^2x) *2 ] 24=02^4x - 10(2^2x) 24 = 02^2x = 6 or 2^2x = 42x = log 6 / log 2 or 2x = 2x = log 6 / 2 log 2 or x = 1
