Section 4.2 Log
Solution: Here the decay constant 2 is 0.00501. By Equa
given by
T =
In 2
In 2
0.00501
~138.4 day
Now
PROBLEMS 4.2
In Problems 1-8, express each logarithmic form exponentially and
57. Appreciation Suppose an anti
each exponential form logarithmically.
year. Graph the number of years it is
1. 104 = 10,000
2. 2 = 10812 144
multiplicative increase in its original
3. log2 1024 = 10
4. 82/3 = 4
the name of the function.
5. e3 ~ 20.0855
6. e0.33647 ~ 1.4
58. Cost Equation The cost for a
7. In 3 ~ 1.09861
8. log 7 ~ 0.84509
product is given by the cost equation
In Problems 9-16, graph the functions.
c = (5q In
9. y =f(x) = log3 X
10. y = f(x) = log4 2x
Evaluate the cost when q = 12. (Ro
11. y =f(x) = log1/4X
12. y = f(x) = log1/5X
decimal places.)
13. y = f(x) = 1082 (x + 4)
14. y = f(x) = 10g2 (-x)
59. Supply Equation A manufact
15. y =f(x) = -2inx
16. y = f(x) = In (x+2)
p = log
In Problems 17-28, evaluate the expression.
17. log6 36
18. log, 512
19. log3 27
where q is the number of units supp
what price will the manufacturer s
20. 10g164
21. log7 7
22. log 10, 000
60. Earthquake The magnitude
23. log 0.0001
24. 10g2 V2
25. logs 1
energy, E, are related by the equati
26. 1085 25
27. log2 8
28. 10g3 V3
In Problems 29-48, find x.
1.5M = log
29. log x = 4
30. log, x = 8
where M is given in terms of Rich
32. logAx = 0
E is in ergs. Solve the equation fo
34. Inx = 1
61. Biology For a certain popu