解方程 $\ln(2x-1)=2\ln(x+1)-\ln x$。答案保留 $3$ 位小数。

Answer all questions. You should use a calculator where appropriate.

You must show all necessary working clearly; no marks will be given for unsupported answers from a calculator.

Give non-exact numerical answers correct to 3 significant figures, or 1 decimal place for angles in degrees, unless a different level of accuracy is specified in the question.

请回答所有题目。适当时应使用计算器。必须清楚展示所有必要的计算过程；仅给出计算器答案而没有过程，不予评分。除非题目另有精度要求，非精确数值答案保留 3 位有效数字，以度为单位的角度保留 1 位小数。

先检查三个对数的定义域，再将右侧合并为商的对数。指数化得到二次方程后，排除不满足定义域的根。

The logarithms require $2x-1>0$, $x+1>0$ and $x>0$, so $x>1/2$.

Using logarithm laws,

Hence

giving

The minus sign gives a negative value and is rejected. Therefore

to 3 decimal places.