The logarithm as a process
Some problems to begin with:
What’s going on here?
power5 125 = 3
power8 64 = 2
power10 0.1 = -1
power81 9 = ½
Your turn
power10 1000 =
power2 64 =
power3 27 =
power7 49 =
power10 1000000 =
power3 81 =
power25 5 =
power2 0.5 =
power10 1 =
power3 3 =
power25 125 =
power36 1/6 =
Watch the video
Learn this…
ab = c ⇔ loga c = b
Convert each of the following facts to logarithmic form
1. 103 = 1000 2. 24 = 16 3. 104 = 10000
4. 32 = 9 5. 42 = 16 6. 52 = 25
7. 10-2 = 0.01 8. 91/2 = 3 9. 50 = 1
10. 41/2 = 2 11. 120 = 1 12. 81/3 = 2
13. p = q2 14. xy = 2 15. pq = r
Convert each of the following facts to index form
16. log10100000 = 5 17. log464 = 3 18. log1010 = 1
19. log24 = 2 20. log232 = 5 21. log101000 = 3
22. log51 = 0 23. log39 = 2 24. log416 = 2
25. log327 = 3 26. log366 = ½ 27. loga1 = 0
28. logxy = z 29. loga5 = b 30. logpq = r
Evaluate
31. log24 32. log101000000 33. log264
34. log381 35. log864 36. log464
37. log93 38. log 1/2 4 39. log100.1
40. log12111 41. log51 42. log22
43. log644 44. log991 45. log273
True or false?
To find loga b
Press
F4 (MATH)
F2 (logab)
eg log28
press F4 then F2
enter 2 then across arrow and enter 8
press EXE
The calculator also has a common logarithm button which is the logarithm to the base 10.
The ln button is the natural logarithm which we will meet in the 3rd lesson.
2? = 6
We know the answer is somewhere between 2 and 3 because 22 = 4 and 23 = 8.
2? = 6 ⇔ ? = log2 6
= 2.58496…
Check you agree with this answer. Also check the answer in the original equation.
6? = 0.25
5? = 0.5
4? = 21
3? = 16
2? = 10
Use your calculator…
2? = -1
2? = 1
0.1? = 2
10? = 62
0.5? = 0.2
Can you arrange some of these logarithms to complete the grid below? The values of the logarithms need to increase along the rows and down the columns. Try to do this without using a calculator.
Try this grid…
Learn this…
ab = c ⇔ loga c = b
extension
Research the history of logarithms.