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11.5 Common Logarithms

11.5 Common Logarithms. By the end of the period, students will be able to use the change of base formula to rewrite logarithms into common logs, and solve equations using common logarithms, as evidenced by completing “Find Someone Who…” worksheet. Assignment #38 Worksheet, no book assignment.

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11.5 Common Logarithms

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  1. 11.5 Common Logarithms By the end of the period, students will be able to use the change of base formula to rewrite logarithms into common logs, and solve equations using common logarithms, as evidenced by completing “Find Someone Who…” worksheet. Assignment #38 Worksheet, no book assignment

  2. By the end of the period, students will be able to use the change of base formula to rewrite logarithms into common logs, and solve equations using common logarithms, as evidenced by completing “Find Someone Who…” worksheet. Common Logarithm • How many fingers do we (normally) have? • What happens after the number 9? • What happens after the number 99? • Why is it easier to multiply by 100 that by 99 even though 99 is a smaller number? • The common log has a BASE of 10. • Since this is our COMMON log we often will write instead of

  3. By the end of the period, students will be able to use the change of base formula to rewrite logarithms into common logs, and solve equations using common logarithms, as evidenced by completing “Find Someone Who…” worksheet. Change of Base Formula • Our calculators only have two log buttons and (we’ll discuss the other button later). • So if we want to use the calculator to solve log problems, we need to have the logs in base 10. New base

  4. By the end of the period, students will be able to use the change of base formula to rewrite logarithms into common logs, and solve equations using common logarithms, as evidenced by completing “Find Someone Who…” worksheet. Example 1: rewrite each expression using the change of base formula

  5. By the end of the period, students will be able to use the change of base formula to rewrite logarithms into common logs, and solve equations using common logarithms, as evidenced by completing “Find Someone Who…” worksheet. Example 1: rewrite each expression using the change of base formula • fill in the blanks:

  6. By the end of the period, students will be able to use the change of base formula to rewrite logarithms into common logs, and solve equations using common logarithms, as evidenced by completing “Find Someone Who…” worksheet. Example 2: Solve each equation using common log • How do we solve ? • Similarly, we can “take the log of both sides” • This power of equality property goes both directions. • Recall that logs and exponents are inverses and will “undo” each other. So if we want to get variable OUT of an exponent we use a log.

  7. By the end of the period, students will be able to use the change of base formula to rewrite logarithms into common logs, and solve equations using common logarithms, as evidenced by completing “Find Someone Who…” worksheet. Example 2: Solve each equation (for ) using common log

  8. By the end of the period, students will be able to use the change of base formula to rewrite logarithms into common logs, and solve equations using common logarithms, as evidenced by completing “Find Someone Who…” worksheet. Example 2: Solve each equation (for ) using common log

  9. By the end of the period, students will be able to use the change of base formula to rewrite logarithms into common logs, and solve equations using common logarithms, as evidenced by completing “Find Someone Who…” worksheet. Example 2: Solve each equation (for ) using common log

  10. By the end of the period, students will be able to use the change of base formula to rewrite logarithms into common logs, and solve equations using common logarithms, as evidenced by completing “Find Someone Who…” worksheet. Find Someone Who… Instructions: • You will not solve a single problem on YOUR paper. • Meet with another person (PAIRS, NOT TRIOS, singles etc. PAIRS!!) • Exchange papers • Look at the unsolved problems on their paper and solve one of your choosing, challenge yourself. • Get your paper back and make a new friend 

  11. By the end of the period, students will be able to use the change of base formula to rewrite logarithms into common logs, and solve equations using common logarithms, as evidenced by completing “Find Someone Who…” worksheet. Summary • Which of the following is equivalent to • Using common logarithms, solve .

  12. By the end of the period, students will be able to use the change of base formula to rewrite logarithms into common logs, and solve equations using common logarithms, as evidenced by completing “Find Someone Who…” worksheet. Summary • Which of the following is equivalent to • Using common logarithms, solve .

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