Use the change of base formula to approximate the following expression. log 38+ log 32 What is the value of log 38 + log 32? (Simplify your answer. Type an integer or a decimal rounded to the nearest thousandth as needed.)Determine the hallrlife of the substance that decays from A0 to A in time t. A=4?, A=20,t=15 years The halflite of the substance is years. (Do not round until the nal answer. Then round to one decimal place as needed.) Solve the exponential equation. Write the exact answer with natural logarithms and then approximate the result correct to three decimal places. 63x +5 = 13 Select the correct choice below and, if necessary, fill in the answer boxes to complete your choice. O A. The exact answer(s) with natural logarithms is/are x = (Type an exact answer in simplified form. Type an integer or a fraction. Use a comma to separate answers as needed.) The approximate answer(s) is/are X ~ (Simplify your answer. Type an integer or a decimal. Round to three decimal places as needed. Use a comma to separate answers as needed.) O B. There is no solution. The solution set is the empty set, O.14 Let f(x) = 3 + ackx with f(0) = 2 and f(1) = > Find a and k and then evaluate the function f(3). The value of a is . (Type an integer or decimal rounded to three decimal places as needed.) The value of k is (Type an exact answer in simplified form. Type an integer or a fraction.) f(3) = (Type an integer or decimal rounded to three decimal places as needed.)25,000 The number of people in a community who became infected during an epidemic t weeks after its outbreak is given by the function f(t) = 1 + ae - kt . Where 25,000 people of the community are susceptible to the disease. Assume that 1000 people were infected initially and 8490 had been infected by the end of the fourth week. Complete parts a. and b.. a. Find the number of people infected after 8 weeks. (Simplify your answer. Do not round until the final answer. Then round to the nearest whole number as needed.) b. After how many weeks will 19,302 people be infected? weeks (Simplify your answer. Do not round until the final answer. Then round to the nearest whole number as needed.)Negative ions, designated by the notation [OH1 are always present in any acid or base The concentrationr [OH _ ] of these ions is related to [H +] by the equation [OHII - [H+] = 10 14 moles per liter. Find the concentrations of [OHII and [H +] in moles per liter forthe substances with the given pH value. sz4 The concentration of [H +] is moles per liter. (Type your answer using exponential notation.) The concentration of [OH _] is moles per liter. (Type your answer using exponential notation.)