Intro to Logarithms

Intro to Logarithms

And how they connect to exponents.

Agenda

• Notes on introduction to logarithms and natural logarithms.

• Homework on logarithms and natural logarithms.

• Stoplight reflection for the week.

Driving Questions

• What is the relationship between logarithms and exponents?

• How are logarithms helping save lives from earthquakes?

Beginning Research. Go to the MathIsFun link in the agenda. For each team:

• 1 person learn about the basics of logarithms.

• 1 person learn about how they connect with exponents.

• 1 person learn about the two "special" logarithms. (base 10 and the natural logarithm.)

• Once you are done: put 2 post it notes on the Jamboard in the agenda.

So, what are logarithms?

• Think this: "How many of one number do we multiply to get another number?"

• For example: how many 3's do we multiply to get 27? 

   $3^{??}=27$  

• The exponent is missing!!!! 

You Try's--- whiteboards with pretty markers.

• How many 4's do we multiply to get 64?

• How many 6's do we multiply to get 7776.

• How many 26's do we multiply to get 1.

• Shoulder partner talk: why does the 26 not matter in the previous question? (for example it could have been 5,000,453,678.)

Common Logarithms in our world.

•  $\log_{10}$ is written as just log. This is what your calculator means by log.

• How many 10's do we multiply to get 1,000? (or  $\log_{10}\left(100\right)$  )

• Plug that into your calculator by just pushing the 'log' button.

Common logarithms in our world.

• Shoulder partner talk: what do you think the base of the 'natural log' is?

• How many ___ do we multiply to get 100? (or  $\ln\left(100\right)$  )

• Plug that into your calculator by pushing the "ln" button.

Well.. how do logarithms and exponents connect?

• Explore in desmos:

•  $2^x$   vs.   $\log_2\left(x\right)$  

•  $e^x\ \ vs.\ \ \ln\left(x\right)$  

•  $10^x\ vs\ \log\left(x\right)$  

• What's that mathematical word that starts with an i again???

Extension

You drink a beverage with 120 mg of caffeine. Each hour, the caffeine in your system decreases by about 12%. How long until you have 10mg of caffeine?