Solve the following logarithmic equations:(要步驟)
1, (log3)(2x-1)=2
2, logx^2=log3x+1
3, (log2)x^3=(log2)4x+2
答案:
1, 5
2, 30
3, 4
log 超緊急.....今日係最後限期!!!!!!!!!!
2010-01-11 4:39 am
回答 (2)
2010-01-11 4:44 am
✔ 最佳答案
(1) log_3 (2x - 1) = 22x - 1 = 3^2
2x - 1 = 9
2x = 10
x = 5
(2) log(x^2) = log(3x) + 1
log(x^2) = log(3x) + log(10)
log(x^2) = log(30x)
x^2 = 30x
x^2 - 30x = 0
x(x - 30) = 0
x = 0 (rejected) or x = 30
(3) log_2 x^3 = log_2 4x + 2
log_2 x^3 = log_2 4x + log_2 4
log_2 x^3 = log_2 16x
x^3 = 16x
x^3 - 16x = 0
x(x + 4)(x - 4) = 0
x = 0 (rejected) or x = -4 (rejected) or x = 4
2010-01-11 9:16 am
(1) log_3 (2x - 1) = 2
2x - 1 = 3^2
2x - 1 = 9
2x = 10
x = 5
(2) log(x^2) = log(3x) + 1
log(x^2) = log(3x) + log(10)
log(x^2) = log(30x)
x^2 = 30x
x^2 - 30x = 0
x(x - 30) = 0
x = 0 (rejected) or x = 30
(3) log_2 x^3 = log_2 4x + 2
log_2 x^3 = log_2 4x + log_2 4
log_2 x^3 = log_2 16x
x^3 = 16x
x^3 - 16x = 0
x(x + 4)(x - 4) = 0
x = 0 (rejected) or x = -4 (rejected) or x = 4
一定
2x - 1 = 3^2
2x - 1 = 9
2x = 10
x = 5
(2) log(x^2) = log(3x) + 1
log(x^2) = log(3x) + log(10)
log(x^2) = log(30x)
x^2 = 30x
x^2 - 30x = 0
x(x - 30) = 0
x = 0 (rejected) or x = 30
(3) log_2 x^3 = log_2 4x + 2
log_2 x^3 = log_2 4x + log_2 4
log_2 x^3 = log_2 16x
x^3 = 16x
x^3 - 16x = 0
x(x + 4)(x - 4) = 0
x = 0 (rejected) or x = -4 (rejected) or x = 4
一定
收錄日期: 2021-04-23 23:26:35
原文連結 [永久失效]:
https://hk.answers.yahoo.com/question/index?qid=20100110000051KK01659