Actividades: 1) Rescher las operaciones indicadas ( 1,5 puntos) a) \( -\frac{1}{6} \sqrt[2]{432}-3 \sqrt[3]{128}+2 \cdot \sqrt[3]{250}=1 p \)

b) \( \sqrt{\frac{2}{3}-\frac{2}{9}}= \)

(5) \( 2 \sqrt{\frac{5}{6}}= \)

Solve the given exponential equation. Express the solution set in terms of natural logarithms or common logarithms. Then use a calculator to obtain a decimal approximation for the solution. \( 3 e^{\mathrm{x}}=53 \) The solution set expressed in terms of logarithms is (Use a comma to separate answers as needed. Simplify your answer. Use integers or fractions for any numbers in the equation.) Now use a calculator to obtain a decimal approximation for the solution. The solution set is \( \{\square\} \). (Use a comma to separate answers as needed. Round to two decimal places as needed.)

3. \( \frac{1}{2} \cdot \log _{3} 81 \)

Complete the conjecture that describes the pattern in the sequence. \( 4,8,12,16,20 \)