解方程 $2^{5-2x}=\frac{4^{x+1}}3$。答案写成 $\frac{\ln a}{\ln b}$ 的形式，其中 $a$ 和 $b$ 为整数。

Answer all questions. Write your answers on the answer booklet. Follow the instructions on the front cover of the answer booklet. If you need additional answer paper, ask the invigilator for a continuation booklet.

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。在答题册上作答，并遵守答题册封面的指示。如需额外答题纸，请向监考人员索取续答册。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。

先将底数 $4$ 改写为 $2^2$，把所有含 $x$ 的指数合并到一边，再取对数。

Since $4^{x+1}=2^{2x+2}$, the equation gives

Dividing by the positive quantity $2^{5-2x}$ and then multiplying by $8$ gives

Taking logarithms, $4x\ln2=\ln24$, so

也可直接对两边取自然对数。利用幂的对数法则整理为一次方程。

Taking logarithms gives

With $\ln4=2\ln2$, rearranging gives

Therefore $x=\ln24/\ln16$.