A logarithmic function has the form of f(x) = 5log x + d where b is the base and d is a constant. The function contains the input-output pairs of (10, 12) and (100, 17). a. Write two equations that could be used to find the values of a and b. b. Find a and b c. Write the equation in the form of f(x) 12. The function k is increasing. The table below gives values for the function at selected values of x. A logarithmic regression y = a + blnx is used to model the data. a. Find the regression model of k k(x) 0.1 -5.3 0.8 1.5 2.1 4.3 1.4 3.4 4.5 6.8 b. What is the value of k(2.5) predicted by the logarithmic function model? 13. Prove, Show, and Justify Given the function g(x) = 2(3)* + 4 Complete the table of values. X 0 1 2 3 4 Notice that the output values are not proportional for the equal-width input-value intervals. Explain how you know that the function is exponential using a semi-log plot. #2 1000 LIM 100 10 0.1 14. Extra Credit: Find the AROC (m) that can be used to find the linear model in the form y = log bx + log a where n = 10. a. Write the linear model equation using the y-intercept on the Semi-log Plot for log a