解方程 $\ln(2x^2-3)=2\ln x-\ln2$，答案用精确形式表示。

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。

先检查对数的定义域，再用对数法则合并右侧。解出的负根会违反 $\ln x$ 的定义域。

The logarithms require $x>0$ and $2x^2-3>0$, hence $x>\sqrt{3/2}$.

Using logarithm laws,

Therefore

The negative root is outside the domain, while $x=\sqrt2$ satisfies it. Hence $\boxed{x=\sqrt2}$.