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Mathematical Investigations III Name: Mathematical Investigations III Logarithms Practice 2 1. 2. 3. 4. 5. Let f x 10 x Let g x log x Domain: Domain: Range: Range: Find the domains of each of the following. h x log 2 x 5 a. b. j x log x 2 3x Find the ranges of each of the following. k x log x 2 a. b. m x log x 1 2 Find: a. log3 34 b. log5 5x 1 c. 2 log2 (32) d. 3log3 (81) Again with f x 10 x and g x log x , find a. g f x b. Logs 8.1 f g x Rev. S03 Mathematical Investigations III Name: 9000 x 2 4 8 16 32 y y 2 16 128 102 4 819 2 8000 7000 6000 5000 Data was collected and plotted. 4000 It was not clear what type of function was represented by this data. 3000 Is it y ax 2 or y ax 3 or y ax 4 ? or is it 2000 exponential, y ab , or some other function entirely? x 1000 0 0 5 10 15 20 25 30 35 Sometimes, we can get a better idea about the nature of the function represented by the data if we use logarithms. Let's create a table that consists of the log of each x value and the log of each y value for each pair of data values. Since there are mostly powers of 2 in the data, let's use log base 2. Complete the table and then graph the resulting ordered pairs of values. U= log2(x) V = log2(y) V log2(y) U log2(x) Find the equation of your new graph in terms of U and V Substitute U log 2 x , and V log 2 y Transform the equation to write y as a function of x, eliminating the logs to determine the function for the original data. Logs 8.2 Rev. S03