✔ 最佳答案
1. log(2x)=log(4x-5)-1
log(2x) = log(4x-5) - log 10
log(2x) = log[(4x-5)/10]
2x = (4x-5)/10
20x = 4x - 5
16x = - 5
x = - 5/16
所以log(2x) = log (- 10/16),負數 take log 無解。
2. log(x^2 +12) / log(x+3) = 2
log(x^2 + 12) = 2log(x+3)
log(x^2 + 12) = log (x+3)^2
x^2 + 12 = (x+3)^2
x^2 + 12 = x^2 + 6x + 9
6x = 3
x = 1/2
3. 3(5^(2x-1))=2^(5x+1)
log 3 + log 5^(2x-1) = log 2^(5x+1)
log 3 + (2x-1)log 5 = (5x+1)log 2
log 3 + (2log5)x - log5 = (5log2)x + log2
(2log5 - 5log2)x = log2 - log3 + log5
xlog(25/32) = log (10/3)
x = log(10/3) / log(25/32)
x = - 4.877146659 = - 4.88
4. (5^(x+2))(7^x)=3
log 5^(x+2) + log 7^x = log 3
(x+2)log5 + xlog7 = log3
x(log5+log7) = log3 - 2log5
x = log(3/25) / log 35
x = - 0.596358921 = - 0.596
5. 3^(2x+1)+3^(2x-1)=8
[3^(2x-1)] (3^2 + 1) = 8
[3^(2x-1) ] 10 = 8
3^(2x-1) = 4/5
(2x-1)log 3 = log (4/5)
2x - 1 = log(4/5) / log 3
2x - 1 = - 0.203114013
x = 0.398442993 = 0.398
2009-11-15 12:55:31 補充：
因為 3^(2x+1)
= 3^(2x-1 + 2)
= 3^2x-1 乘 3^2 (拆指數)
3^(2x+1)+3^(2x-1)=8
[3^(2x-1)] * (3^2) + [3^(2x-1)] * 1 = 8
[3^(2x-1)] (3^2 + 1) = 8 (抽個 3^(2x-1),因式分解)
