Advanced Algebra II Solve each equation (Non-­‐Calculator) Exponential and Logarithms Test Review 1
243
1
64
6. 5
2. 3x =
4. 625x = 125 5. 256 x =
1. 2x = 128 3. 27x = 3 3x + 1
= 252x 4x
x – 3 7. 4 = 16
8. Write in logarithmic form: ax = y Evaluate (Non-­‐Calculator) 10. log 6 36 18. log 10 1
125
11. log 5
15. 5
19. ln e-­‐2 14. log8 1 log5 10
9. Write in exponential form: log z
12. log 343 7 16. e
ln 3
w = y 1
25
13. log125
17. - log9 9 20. Write an exponential function of the form y = abx that includes the points (1,2) and (2, 8) (Calculator) 21. You put $2000 into an account earning 4% interest compounded continuously. Find the amount at the end of 8 years. (Calculator) 22. Write each equation in logarithmic form. 23. Write in exponential form: 1
a. 53 = 125 b. 41/2 = 2 a. log9 81 = 2 b. log16 4 = 2
24. Solve each equation. Round to the nearest hundredth. (Calculator) a. 4x = 9 b. 6 + 3x+1 = 18 c. ln5x = 4 d. 3ex – 5 = 10 25. Identify each equation as either exponential growth or decay. Then find the annual percent increase or decrease. (Calculator) a. y = 6(1.08)x b. y = 3(.80)x x
æ 5 ö
c. y = ç ÷ è 4 ø
d. y = 6(.83)x 26. Sketch the graph. Include any intercepts, asymptotes, and one other point. (This portion will be non-­‐
calculator) x
a. y = 3 × 2 x
c. y = log3 x æ 1 ö
b. y = 4 ç ÷ è 2 ø
d. y = ln x think about what the base is!) 27. Suppose that the number of bacteria in a culture in your biology lab is increasing exponentially with time. On Tuesday there are 2000 bacteria. On Thursday the number has increased to 4500. a. Derive the particular equation b. Predict the number of bacteria that will be in the culture on Tuesday of the next week. c. Predict the time when the bacteria will reach 10,000. d. Draw the graph of the function.