f) (3 points) Provide the correct property that justifies collapsing to a single logarithm. n logi(x) + mlog (y) - plog.(z) = 1ogb (2" ) + log. (ym) - 10go (zP) = logo(zym) - logo(2P) = ZP g) (4 points) Fully collapse: , log(r + 1) - 3log(x - 1) + log(2). h) (4 points) Suppose F(x) = log3(x - 272) + 3. If F(x) = 9, find x.5. Solving exponential equations. a) (4 points) Give the Steps to Solve Exponential Equations by Using Logarithms. This statement must be written verbatim from the textbook, page 669. Step 1: Isolate the exponential expression on one side of the equation. Step 2: Take a logarithm of the same base on both sides of the equation Step 3: use the power property of logarithms to "bring down" the exponent. Step 4: Solve the resulting equation. b) (4 points) Determine how long it will take $25,500 compounded monthly at 1.5% interest to triple. Show all four steps as listed in part a. Round to the nearest year. c) (6 points) Given the functions g(x) = etz and h(x) = 3et + 10 find all real number solutions for which g(x) = h(x). Write the solution set with exact values given in terms of natural logarithms.6. Solving logarithmic equations. a) (5 points) Give the steps for Solving Logarithmic Equations by Using Exponential Form. This statement must be written verbatim from the textbook, page 678. Step 1: Given a logarithmic equation, isolate the logarithms on one side of the equation. Step 2: Use the properties of logarithms to write the equation in the form log,x = k, where K is a constant. Step 3: write the equation in exponential form Step 4: Solve the equation from the step 3 Step 5: Check the potential solution (s) in the original equation b) (5 points) A new teaching method to teach math to adults involves having students com- plete a take home project to learn algebra. After the project was completed, the students were tested at 1-month intervals. The average score for the class S(t) can be modeled by S(t) = 94 - 18 In(t + 1) where t is the time in months after completing the project. If the average score is 65, how many months had passed since the students completed the project? Show all five steps as listed in part a. Round to the nearest month. c) (5 points) Given the functions f(x) = log(-x) + log(3) and g(x) = log(10 - 4x) - log(2) find all real number solutions for which g(x) = f(x). Write the solution set with exact values.7. Because we need to make sure mathematics has real world applications... The level of irritation a student feels while completing a take home project, that they felt would be an easy A, can be measured on a scale from 0-10, where 0 is no irritation at all and 10 is the most irritation one could ever experience in their entire life. When the student hands in their project, the rate at which the level of irritation reduces over time, t in days, after turning the project in, can be modeled by I(t) = -210g2(t + 1) + 8. a) (1 point) What is the level of irritation when the student hands in their project, i.e. t = 0? b) (1 point) What is the I(t)-intercept. Write your answer as an ordered pair. c) (1 point) What is the level of irritation 7 days after handing in the project? d) (2 points) What day does the level of irritation reach zero? e) (3 points) Graph the function. Make sure to label the t-axis and the I(t)-axis. This is a curve so do not draw straight lines. f) (2 points) Give the domain of the model in interval notation. Take into account how this model is applied in the real world. 9) (2 points) Give the range of the model in interval notation. Take into account how this model is applied in the real world