解方程 $2(3^{2x-1})=4^{x+1}$，答案精确到小数点后 2 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。

直接取对数，用幂的对数法则把指数变成乘数，再解一次方程。

Taking natural logarithms,

Thus

Hence

Therefore $\boxed{x=2.21}$ to 2 decimal places.

先用指数法则合并含 $x$ 的项，化成一个指数方程再取对数。

Rearranging with the laws of indices,

Taking logarithms,

Therefore

to 2 decimal places.