A Tutorial on Logarithms Chapter 8 Section 8.5

1. A Tutorial on LogarithmsChapter 8 Section 8.5 Have your notes and text open to logarithms for reference. Have pencil and paper ready. Write down questions you wish to ask your teacher.

2. Logarithm RulesThese rules are important. You need to master them before you try to solve logarithmic equations. Apply them to the problems on the next 5 slides to see if you understand. • ln A.B = ln A + ln B • loga x.y = loga x + loga y • ln x/y = ln x - ln y • logax/y = loga x - loga y • ln xb = b.ln x • loga xb = b.loga x Have your paper and pencil ready! Feel free to THINK!!!!

3. Read directions carefully then solve the problem. Write out each step on your paper. As you complete a step, click on the to see the correct response. If yours is correct, move on to the next step. If yours is not correct, read the explanation. Condense the following expression. ln 5 – ln 9 + 2 ln 3 ln 5 – ln 9 + ln 32 The 2 in front of the ln is the exponent for 3. Write it as an exponent. Example: 3 ln 5 is ln 53. Once exponents are taken care of, apply properties from left to right. ln A – ln B is equivalent to ln (A/B) ln (5/9) + ln 32 The next property is +. ln C + ln D is equivalent to ln C . D …also 3 squared is 9. ln (5/9) . (9) The final step is simple arithmetic. 5 /9 . 9 is 5 ln 5

4. Read directions carefully then solve the problem. Write out each step on your paper. As you complete a step, click on the to see the correct response. If yours is correct, move on to the next step. If yours is not correct, read the explanation. Condense the following expression. log3 5 + log3 9 + 4 log3 3 The 4 in front of the log is the exponent for 3. Write it as an exponent. Example: 3 ln 5 is ln 53 . You must recognize that 9 is a power of 3, the base of the log. log3 5 + log3 32 + log3 34 Once exponents are taken care of, apply properties from left to right. Notice that 9 is 32 . The base is 3, Sothe log of 32 to the base of 3 is 2!! the same is true of the next term. It simplifies to 4. log3 5 + 2 + 4 log3 5 + 6 The next property is arithmetic …….. 2 + 4 =6 ….. Note the first term cannot be simplified any further. 5 is not a power of 3, the base.

5. Read all directions.Write the steps on paper then click the to see the correct response. If yours is correct, go to the next step If it is not, read the explanation. Write the expression in expanded form. Show each step. ln 3x2 The logarithm of a product may be rewritten as the sum of 2 logs. ln A . B is ln A + ln B. Do not do the exponent first. The 2 goes only with the x. ln 3 + ln x2 ln 3 + 2 ln x The logarithm of a power may be rewritten as a product ln Cd = d . ln C

6. Read all directions.Write the steps on paper then click the to see the correct response. If yours is correct, go to the next step If it is not, read the explanation. Write the expression in expanded form. Show each step. log5 ( (3x4)/7 ) The logarithm of a quotient may be rewritten as the difference of 2 logs. ln A /B is ln A - ln B. log5 3 x4 - log5 7 log5 3 + log5 x4 - log5 7 The logarithm of a product may be rewritten as the sum of 2 logs. ln A.B is ln A + ln B. The logarithm of a power may be rewritten as a product ln Cd = d . ln C log5 3 + 4 log5 x - log5 7

7. condense: 5 log y + 3 log 10 condense: ln 64 + 2 ln ¼ - ln 4 expand: log4 64y4 expand: ln 3xy3 log 1000y5 0 3 + 4 log4 y ln 3 + ln x + 3 ln y What did you learn????Condense and expand the expressions in the left column as directed.Click the in the right column for the answer. click me! Want extra credit? Ask your teacher for a survey on how to improve this tutorial. End