作业帮log(9)x+log(x^2)3=1的解为?原方程可可化为log(3 ²)x+log(x)²3=1 ,∴1/2*log(3)X+1/2*log(x)3=1,∴[log(3)x]²-2log(x)3+1=0,即[log(3)x-1]²=0请问这里的[log(3)x]²-2log(x)3+1=0是怎么推出来的,刚学基础不好,
来源：学生作业帮助网 编辑：作业帮 时间：2024/04/19 01:33:22
![log(9)x+log(x^2)3=1的解为?原方程可可化为log(3 ²)x+log(x)²3=1 ,∴1/2*log(3)X+1/2*log(x)3=1,∴[log(3)x]²-2log(x)3+1=0,即[log(3)x-1]²=0请问这里的[log(3)x]²-2log(x)3+1=0是怎么推出来的,刚学基础不好,](/uploads/image/z/5263347-3-7.jpg?t=log%289%29x%2Blog%28x%5E2%293%3D1%E7%9A%84%E8%A7%A3%E4%B8%BA%3F%E5%8E%9F%E6%96%B9%E7%A8%8B%E5%8F%AF%E5%8F%AF%E5%8C%96%E4%B8%BAlog%283+%26%23178%3B%29x%2Blog%28x%29%26%23178%3B3%3D1+%2C%E2%88%B41%2F2%2Alog%283%29X%2B1%2F2%2Alog%28x%293%3D1%2C%E2%88%B4%5Blog%283%29x%5D%26%23178%3B-2log%28x%293%2B1%3D0%2C%E5%8D%B3%5Blog%283%29x-1%5D%26%23178%3B%3D0%E8%AF%B7%E9%97%AE%E8%BF%99%E9%87%8C%E7%9A%84%5Blog%283%29x%5D%26%23178%3B-2log%28x%293%2B1%3D0%E6%98%AF%E6%80%8E%E4%B9%88%E6%8E%A8%E5%87%BA%E6%9D%A5%E7%9A%84%2C%E5%88%9A%E5%AD%A6%E5%9F%BA%E7%A1%80%E4%B8%8D%E5%A5%BD%2C)
log(9)x+log(x^2)3=1的解为?原方程可可化为log(3 ²)x+log(x)²3=1 ,∴1/2*log(3)X+1/2*log(x)3=1,∴[log(3)x]²-2log(x)3+1=0,即[log(3)x-1]²=0请问这里的[log(3)x]²-2log(x)3+1=0是怎么推出来的,刚学基础不好,
log(9)x+log(x^2)3=1的解为?
原方程可可化为log(3 ²)x+log(x)²3=1 ,∴1/2*log(3)X+1/2*log(x)3=1,∴[log(3)x]²-2log(x)3+1=0,即[log(3)x-1]²=0
请问这里的[log(3)x]²-2log(x)3+1=0是怎么推出来的,刚学基础不好,感谢ing……
log(9)x+log(x^2)3=1的解为?原方程可可化为log(3 ²)x+log(x)²3=1 ,∴1/2*log(3)X+1/2*log(x)3=1,∴[log(3)x]²-2log(x)3+1=0,即[log(3)x-1]²=0请问这里的[log(3)x]²-2log(x)3+1=0是怎么推出来的,刚学基础不好,
因为log(x)3与log(3)X是互为倒数关系,
所以,在方程1/2*log(3)X+1/2*log(x)3=1两边同乘1/2*log(x)3,
即可得到：[log(3)x]²+1=2log(3)x ,
移项,得：[log(3)x]²-2log(3)x +1=0,
这里：[log(3)x]²-2log(x)3+1=0,——你打错了.
也可以这样：log(3)x+log(x)3=2
log(3)x+log(x)3=log(3)3+log(x)x
log(3)x-log(3)3=log(x)x-log(x)3
log(3)(x-3)=log(x)(x-3)
x=3你好，谢谢你的答案，但我想问下。如果log(3)x-log(3)3=log(x)x-log(x)3有 log(3)(x-3)=log(x)...
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也可以这样：log(3)x+log(x)3=2
log(3)x+log(x)3=log(3)3+log(x)x
log(3)x-log(3)3=log(x)x-log(x)3
log(3)(x-3)=log(x)(x-3)
x=3
收起
此题用均值不等式来解最好：log(9)x+log(x^2)3=[log(3)x+log(x)3]/2=1，log(3)x+log(x)3=2，因为log(3)x与log(x)3互为倒数，所以log(3)x与log(x)3同号，显然依题意有log(3)x与log(x)3同为正数，log(3)x+log(x)3>=2当log(3)x=log(x)3，即log(3)x=log(x)3=1，此为x=3
333333
不对啊