高一对数和指数方程题目1.方程x^(lgx-3) =1/100 2.对数方程log3(x-1) =log9(x+1) 3.己知实数x,y满足lg(x-y) + lg(x+2y) = lg2 + lgx + lgy,求x/y=
来源:学生作业帮助网 编辑:作业帮 时间:2024/07/06 23:45:16
![高一对数和指数方程题目1.方程x^(lgx-3) =1/100 2.对数方程log3(x-1) =log9(x+1) 3.己知实数x,y满足lg(x-y) + lg(x+2y) = lg2 + lgx + lgy,求x/y=](/uploads/image/z/6848099-35-9.jpg?t=%E9%AB%98%E4%B8%80%E5%AF%B9%E6%95%B0%E5%92%8C%E6%8C%87%E6%95%B0%E6%96%B9%E7%A8%8B%E9%A2%98%E7%9B%AE1.%E6%96%B9%E7%A8%8Bx%5E%28lgx-3%29+%3D1%2F100+2.%E5%AF%B9%E6%95%B0%E6%96%B9%E7%A8%8Blog3%28x%EF%BC%8D1%29+%3Dlog9%28x%2B1%29+3.%E5%B7%B1%E7%9F%A5%E5%AE%9E%E6%95%B0x%2Cy%E6%BB%A1%E8%B6%B3lg%28x-y%29+%2B+lg%28x%2B2y%29+%3D+lg2+%2B+lgx+%2B+lgy%2C%E6%B1%82x%2Fy%3D)
高一对数和指数方程题目1.方程x^(lgx-3) =1/100 2.对数方程log3(x-1) =log9(x+1) 3.己知实数x,y满足lg(x-y) + lg(x+2y) = lg2 + lgx + lgy,求x/y=
高一对数和指数方程题目
1.方程x^(lgx-3) =1/100
2.对数方程log3(x-1) =log9(x+1)
3.己知实数x,y满足lg(x-y) + lg(x+2y) = lg2 + lgx + lgy,求x/y=
高一对数和指数方程题目1.方程x^(lgx-3) =1/100 2.对数方程log3(x-1) =log9(x+1) 3.己知实数x,y满足lg(x-y) + lg(x+2y) = lg2 + lgx + lgy,求x/y=
1.两边取对数
(lgx-3)*lgx=-2
(lgx)²-3lgx+2=0
(lgx-2)(lgx-1)=0
解得lgx=2 x=100
或lgx=1 x=10
2.显然x-1>0 则x>1
log9 (x-1)²=log9 (x+1)
x²-2x+1-x-1=0
x²-3x=0
解得x=0(舍去)或x=3
3.显然xy>0 即x,y同号
lg (x-y)(x+2y)=lg 2xy
则 x²+xy-2y²=2xy
x²-xy-2y²=0
(x-2y)(x+y)=0
解得x-2y=0 则x/y=2
或x+y=0(因x,y异号,舍去)
1.x^(lgx-3) =1/100 两边取对数,lgx*(lgx-3)=-2 解出lgx=1,x=10
2.log3(x-1) =log3根号下(x+1) ,x-1=跟号下x+1 两边平方(x-1)^2=x+1 ,x=0
3.lg(x-y) + lg(x+2y)=lg(x-y)(x+2y),lg2 + lgx + lgy=2xy
(x-y)(x+2y)=2xy,两边同时...
全部展开
1.x^(lgx-3) =1/100 两边取对数,lgx*(lgx-3)=-2 解出lgx=1,x=10
2.log3(x-1) =log3根号下(x+1) ,x-1=跟号下x+1 两边平方(x-1)^2=x+1 ,x=0
3.lg(x-y) + lg(x+2y)=lg(x-y)(x+2y),lg2 + lgx + lgy=2xy
(x-y)(x+2y)=2xy,两边同时除以y^2 ,(x/y-1)(x/y+2)=2x/y,x/y=-1(舍去)因为x,y都为正 x/y=2
收起
第一题符号没看懂
第二题0或3
第三题-2或1