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Part 1 - Application The magnitude R (on the Richter scale) of an earthquake of Intensity / is defined as R = log To where Io = minimum intensity used for comparison. Ms. Cohen felt an earthquake in Los Angeles that had an intensity of (5 x 10") (To). What was its magnitude, to one decimal place, on the Richter scale? Be sure to show and explain your work, including breaking down the logarithm into its separate parts.Part 2 - Find the error(s) and solve the problem correctly. Solve. Be sure to show and explain your work. logA (x + 3) + log, (x - 3) = 2 Answer: log (x + 3) + log (x - 3) = 2 log(x +3+ x - 3) = 2 log (2x) = 2 42 = 2x 16 = 2x 8 =0Part 3 - Discussion Question How do we know that e" and In are inverses of each other?Chemical Acidity In chemistry, the acidity of a water-based solution is measured by the concentration of hydrogen ions in the solution (in moles per liter). The hydrogen-ion concentration is written [H ]. Because such concentrations usually involve negative powers of ten, negative orders of magnitude are used to compare acidity levels. The measure of acidity used is ph, the opposite of the common log of the hydrogen-ion concentration: PH =- log[H*] More acidic solutions have higher hydrogen-ion concentrations. A certain brand of lemon juice has a ph of 2.1, and a certain brand of cleaning ammonia has a ph of 11.6. a) Find the hydrogen-ion concentrations for the lemon juice and the ammonia. b) How many times greater Is the hydrogen-ion concentration of the lemon juice than the ammonia?Newton's Law of Cooling An object that has been heated will cool to the temperature of the environment in which it is placed, such as the surrounding air or water. The temperature of the object at time can be modeled by the equation T(t ) = T. +(To -T. )e -ke for an appropriate value of k, where T = the temperature of the surrounding environment T = initial temperature of the object This model is called Newton's Law of Cooling. A hard-boiled egg at temperature 92 is placed in 20 water to cool. Five minutes later, the temperature of the egg is 45" . a) Use the given information to solve for k. b) Use Newton's Law of Cooling to determine when the temperature of the egg will be 30. Round your answer to the nearest hundredth of a minute.Solving Equations Solve each equation using the method of your choice. Give each solution in two forms: exact and rounded to the nearest hundredth. Be sure to fully justify your response by showing all work and/or explaining your reasoning in detail. a) 2e "+ 5e- 3 = 0 (Hint: let u = e , and factor the resulting quadratic equation). b) log(x - 2) + log(x + 5) = 2log(3)