解方程

最终答案保留 $4$ 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。

先移项并指数化，再解指数方程。原对数要求 $x>0$，最后核对结果。

The logarithm requires $1-e^{-2x}>0$, so $x>0$.

From the equation,

Thus

and taking logarithms gives

to 4 decimal places. This is positive and satisfies the original domain.