Simplify the radical expression by factoring out the largest perfect nth power. Assume that all variables are positive. 25) \( \sqrt{245 x^{2}} \) If possible, simplify the expression and combine like terms. If any variables exist, assume that they are positive. 26) \( -8 \sqrt{2}-7 \sqrt{50} \) Multiply, then simplify the product. If variables are present, assume they are positive. \( 27)(\sqrt{2}-6)(\sqrt{5}-2) \)

Use the properties of logarithms to expand the following expression. \[ \log \left(\frac{x^{5}}{\sqrt{(x+6)^{3}}}\right) \] Your answer should not have radicals or exponents. You may assume that all variables are positive.

(6) \( \frac{9}{2} \sqrt{\frac{5}{3}}= \)

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

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

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.)