Logarithms Logarithms

ObjectiveObjective

To have an understanding of the history To have an understanding of the history of logarithms, and to be able to change of logarithms, and to be able to change exponential equation into logarithmic exponential equation into logarithmic equations. equations.

What are they used What are they used for???for???

you can use logarithms in many you can use logarithms in many statistics, biology, physics, and chemistry statistics, biology, physics, and chemistry concepts to solve different problems. And concepts to solve different problems. And In recent times, Math scholars and In recent times, Math scholars and students use logarithms to solve students use logarithms to solve exponential equations and to solve exponential equations and to solve numbers extending from very big to small numbers extending from very big to small expression in a more refined manner. expression in a more refined manner.

When changing When changing exponents to logs…exponents to logs…

1. Use the equation log1. Use the equation logaa(n)=b(n)=b2. Then, for a, substitute in the base of the exponent2. Then, for a, substitute in the base of the exponent3. For b, substitute in the exponent3. For b, substitute in the exponent

Ex1) Change 4Ex1) Change 43 3 into logarithmic forminto logarithmic form loglogaa(n)=b (n)=b loglog44(n)=b (n)=b loglog44(n)=3(n)=3*since 4*since 43 3 is 64, 4is 64, 43 3 in logarithmic form isin logarithmic form isloglog44(64)=3(64)=3

When changing a log When changing a log into an exponential into an exponential equation…equation…

1. Use the equation a1. Use the equation abb=n=n2. For a, substitute in the subscript of log2. For a, substitute in the subscript of log3. For b, substitute in the answer of the log3. For b, substitute in the answer of the log

Ex.2) Change logEx.2) Change log22(n)=3 (n)=3

aabb=n =n 22bb=n =n 2233=n=nn=8n=8

GAME!!!GAME!!!

How to play…How to play… Each row will receive a paper, therefore each row is Each row will receive a paper, therefore each row is

a teama team The first person will start, and solve the first The first person will start, and solve the first

problem.problem. When he or she is done, pass it to the next person.When he or she is done, pass it to the next person. That person can either fix the problem done That person can either fix the problem done

previously, or go on to the next.previously, or go on to the next. The first row to finish the paper correctly will win.The first row to finish the paper correctly will win.

When you are done with When you are done with the game…the game…

Summary: today I learned… Summary: today I learned…

Don’t forget to do the worksheet!!! :] Don’t forget to do the worksheet!!! :]