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### Transcript of Intro to Logs

• 1. Introduction To Logarithms

2. Our first question then must be: What is a logarithm ? 3. Definition of Logarithm Suppose b>0 and b1,there is a number psuch that: 4. You must be able to convert an exponential equation into logarithmic form and vice versa. So lets get a lot of practice with this ! 5. Example 1: Solution: We read this as: the log base 2 of 8 is equal to 3. 6. Example 1a: Solution: Read as: the log base 4 of 16 is equal to 2. 7. Example 1b: Solution: 8. Okay, so now its time for you to try some on your own. 9. Solution: 10. Solution: 11. Solution: 12. It is also very important to be able to start with a logarithmic expression and change this into exponential form. This is simply the reverse ofwhat we just did. 13. Example 1: Solution: 14. Example 2: Solution: 15. Okay, now you try these next three. 16. Solution: 17. Solution: 18. When working with logarithms, if ever you get stuck, try rewriting the problem in exponential form. Conversely, when working with exponential expressions, if ever you get stuck, try rewriting the problem in logarithmic form. 19. Solution: Lets rewrite the problem in exponential form. Were finished ! Example 1 20. Solution: Rewrite the problem in exponential form. Example 2 21. Example 3 Try setting this up like this: Solution: Now rewrite in exponential form. 22. Properties of logarithms 23.

• Let b, u, and v be positive numbers such that b 1.
• Product property:
• log b uv = log b u + log b v
• Quotient property:
• log b u/v = log b u log b v
• Power property:
• log b u n= n log b u

24. Expanding Logarithms

• You can use the properties to expand logarithms.
• log 27x 3/ y= log 2 7x 3- log 2 y =
• log 2 7 + log 2 x 3 log 2 y =
• log 2 7 + 3 log 2 x log 2 y

25.

• Expand:
• log 5mn =
• log 5 + log m + log n
• Expand:
• log 5 8x 3=
• log 5 8 + 3 log 5 x

26. Condensing Logarithms

• log 6 + 2 log2 log 3 =
• log 6 + log 2 2 log 3 =
• log (6 2 2 ) log 3 = log 24 log 3=
• log 24/3=log 8

27.

• Condense:
• log 5 7 + 3 log 5 t = log 5 7t 3
• Condense:
• 3log 2 x (log 2 4 + log 2 y)= log 2x 3 /4y

28. Change of base formula:

• u, b, and c are positive numbers with b 1 and c1.
• Then:
• log c u = log u / log c (base 10)

29. Examples:

• Use the change of base to evaluate:
• log 3 7 =
• log 71.771
• log 3