求满足不等式 $|2^{x+1}-2|<0.5$ 的 $x$ 的取值范围，答案保留 $3$ 位有效数字。

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。

把绝对值不等式化成双边不等式。底数 $2>1$，取对数后不等号方向不变。

The inequality is equivalent to

so

Taking logarithms and dividing by $\ln2>0$ gives

Therefore

The boundary values are $-0.415037\ldots$ and $0.321928\ldots$. Thus, to 3 significant figures,