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11.5 Common Logarithms By the end of the period, students will be able to use the change 11.5 Common Logarithms By the end of the period, students will be able to use the change

11.5 Common Logarithms By the end of the period, students will be able to use the change - PowerPoint Presentation

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11.5 Common Logarithms By the end of the period, students will be able to use the change - PPT Presentation

Assignment 38 Worksheet no book assignment 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 ID: 692357

logarithms common base solve common logarithms solve base change formula rewrite logs find worksheet who

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Slide1

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 assignmentSlide2

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

 

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.Slide3

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

.

 

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.

New baseSlide4

Example 1: rewrite each expression using the change of base formula

 

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.Slide5

Example 1: rewrite each expression using the change of base formula

fill in the blanks:

 

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.Slide6

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. 

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.Slide7

Example 2: Solve each equation (for

) using common log

 

 

 

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.Slide8

Example 2: Solve each equation (for

) using common log

 

 

 

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.Slide9

Example 2: Solve each equation (for

) using common log

 

 

 

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.Slide10

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 

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

.Slide11

Summary

Which of the following is equivalent to

Using common logarithms, solve

.

 

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.Slide12

Summary

Which of the following is equivalent to

Using common logarithms, solve

.

 

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.