9^x-2 = 4^3-2x
solve this equation.
Maths (log) .....
2006-10-17 6:30 am
回答 (4)
2006-10-17 6:49 am
✔ 最佳答案
9^(x-2) = 4^(3-2x)=> log 9^(x-2) = log 4^(3-2x)
=> (x-2) (log 9) = (3-2x) (log 4)
=> (log 9) x - 2 (log 9) = 3 (log 4) -2(log 4)x
=> (log 9) x + (log 16) x = (log 81) + (log 64)
=> x = [(log 81) + (log 64)] / [(log 9) + (log16)]
=> x = (log 5184) / (log 144)
=> x = 1.72
2006-10-17 8:01 am
Solution
9^(x-2) = 4^ (3-2x)
3^ [2(x-2)] = 2^ [2(3-2x)]
3^ (2x-4) = 2^(6-4x)
log3^ (2x-4) = log 2^(6-4x)
(2x – 4) log3 = (6 - 4x) log2
2xlog3 – 4log3 = 6log2 –4xlog2
2xlog3 +4xlog2 = 6log2 +4log3
xlog3 +2xlog2 = 3log2 +2log3
x (log3 +2log2) = 3log2 +2log3
x = (3log2 +2log3) / (log3 +2log2)
x=1.72106
9^(x-2) = 4^ (3-2x)
3^ [2(x-2)] = 2^ [2(3-2x)]
3^ (2x-4) = 2^(6-4x)
log3^ (2x-4) = log 2^(6-4x)
(2x – 4) log3 = (6 - 4x) log2
2xlog3 – 4log3 = 6log2 –4xlog2
2xlog3 +4xlog2 = 6log2 +4log3
xlog3 +2xlog2 = 3log2 +2log3
x (log3 +2log2) = 3log2 +2log3
x = (3log2 +2log3) / (log3 +2log2)
x=1.72106
參考: myself
2006-10-17 6:43 am
9^x-2 = 4^3-2x
3^(2x-4)=2^(6-4x)
log3^(2x-4)=log2^(6-4x)
2xlog3-4log3=6log2-4xlog2
2x(log3+2log2)=6log2+4log3
x=(2log3+3log2)/(log3+2log2)
3^(2x-4)=2^(6-4x)
log3^(2x-4)=log2^(6-4x)
2xlog3-4log3=6log2-4xlog2
2x(log3+2log2)=6log2+4log3
x=(2log3+3log2)/(log3+2log2)
參考: me
2006-10-17 6:43 am
9^(x-2)=4^(3-2x)
3^[2(x-2)]=2^[2(3-2x)]
[2(x-2)]log3=[2(3-2x)]log2
1.585(x-2)=3-2x
3.585x=6.17
x=1.721
3^[2(x-2)]=2^[2(3-2x)]
[2(x-2)]log3=[2(3-2x)]log2
1.585(x-2)=3-2x
3.585x=6.17
x=1.721
收錄日期: 2021-04-12 22:51:12
原文連結 [永久失效]:
https://hk.answers.yahoo.com/question/index?qid=20061016000051KK04851