解方程 $\ln(\mathrm{e}^{2x}+3)=2x+\ln3$，答案精确到小数点后 3 位。

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。

将右侧写成 $\ln(3e^{2x})$，再去掉两边的对数得到指数值，最后取对数求 $x$。

Since $2x=\ln(e^{2x})$,

Thus

Taking logarithms,

to 3 decimal places.