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Transcript
e/ Natural Log
Starting with the graph y = ex, write and equation of the graph that results from
1. shifting 2 units down
2. shifting 2 units right
3. reflecting about the x-axis
4. reflecting about the y-axis
Find the inverse function of
5. y = ln(x + 3)
6. y = 2(x + 3)
Express as a single logarithm
7. 2 ln 4 - ln 2
8. ln x + a ln y - b ln z
Evaluate each logarithm to six decimal places
9. log25
10. log526.05
Solve each equation for x
11. ex = 16
12. ln x = -1
13. ln(2x – 1) = 3
14. e(3x – 4) = 2
15. 2(x-5) = 3
16. ln x + ln(x -1) = 1
17. ln(ln x) = 1
18. If a bacteria population starts with 100 bacteria and doubles every three hours,
then the number of bacteria after t hours is n = f(t) = 100 ∙ 2t/3
a) find the inverse function
b) how many hours will it take for the population to reach 50,000?