解方程 $\ln5+\ln(3x-2)=2\ln(x-4)$。答案写成化简后的精确形式。

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。

先检查对数的定义域，再合并对数。解二次方程后须排除不符合原定义域的根。

The logarithms require $x>4$. Combining them gives

Removing the logarithms and expanding gives

The discriminant is $23^2-4(26)=425=25\times17$, so the roots are $(23\pm5\sqrt{17})/2$. The smaller is less than $4$, so the solution is