Exponential and Logarithmic Function

Exponential and Logarithmic Function

1. Determine the exact value of the following logarithms. You must show ALL work to receive credit for this problem. (a) log, 64 (b) In(e2020) (c) log, 10+log, 25 – log 2

2. Solve the following equations for x. 6x-3 (a) 2e = 8 (b) 2 log2 (x - 1) – log, 9 = 2

3. State the domain of the following functions. a) f(x) = logo (3x – 7) b)f(x) = ln(5 – x)

4. Write an equation for the exponential function y = 7* function that has been reflected about the x axis and shifted horizontally to the right 4 units. Sketch the graph of this function and state the domain and range of this function. Make sure you label any asymptotes on your graph! 4 3 1 A + 1 + + 3 4 + 5 _5 4 -3 -2 2 -1 -2 + -3- Function: Domain: Range:

5. Write an equation for the logarithmic function y = log2x function that has been reflected about the y axis and shifted Vertically to the up 2 units. Sketch the graph of this function and state the domain and range of this function. Make sure you label any asymptotes on your graph! 5 4+ 1 + + 1 { A++++ + -5 -4 -3 -2 -1 -1 1 2 3 4 5 x -2 + -3- -4- Function: Domain: Range: