Instructions: Hand-write your responses on lined paper using proper log notation. Include all steps and show all your work.
1. Expand the logarithmic expression: log(x2 y5)
2. Condense the logarithmic expression: 2log(x) - 3log(y) + log(5)
3. Solve for x: log4 (22) = x
4. Solve for x: 16(x + 1) = 4(3x)
5. The population in Small Town, USA, is 5,000, and expected growth is 3% each year over 10 years. What is the total population after 10 years?
6. If you want to save $12,000 in seven years and believe you can invest at 7% interest, how much is your initial deposit?
7. Sketch the following exponential functions (Note: you do not need to plot these accurately):
a. f(x) = 2x + 2
b. f(x) = 2-x - 1
c. f(x) = 2x - 3
8. Find the inverse function of: f(x) = log4 (x+1) - 2
9. Sketch the following logarithmic functions:
a. f(x) = log2 (x + 4)
b. f(x) = log2 (-x) - 1
10. Use the change of base formula to evaluate to two decimal places: log7 (100)
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