Logs Day 1 TUESDAY FEBRUARY 2 2016 ADAPTED

Logs Day 1 TUESDAY, FEBRUARY 2, 2016 ADAPTED FROM: HTTP: //MATHEQUALSLOVE. BLOGSPOT. COM/2014/01/INTRODUCING-LOGARITHMSWITH-FOLDABLES. HTML

Essential Question How do I convert an exponential equation to a logarithmic equation and vice versa?

What is a logarithm? A logarithm is just a special way to ask a specific question. The Question: What exponent is required to go from a base of b to reach a value of a? “log base b of a is x”

Exponential Form exponent answer base = Logarithmic Form logbaseanswer= expone

Anytime the base of a logarithm is not written, it is assumed to be the number 10. E

The Logarithm Loop Trick Always draw your loop counter-clockwise from the base!

Let’s Practice!

Example 1: Solution: We read this as: ”the log base 2 of 8 is equal to 3”.

Example 1 a: Solution: Read as: “the log base 4 of 16 is equal to 2”.

NOTE: Logarithms can be equal to negative numbers BUT… The base of a logarithm cannot be negative… NOR can we take the log of a negative number!! Example 1 b: Solution:

Okay, so now it’s time for you to try some on your own.

Solution:

Solution:

Solution:

It is also very important to be able to start with a logarithmic expression and change this into exponential form. This is simply the reverse of what we just did.

Example 1: Solution:

Example 2: Solution:

Okay, now you try these next three. Solution:

Solution:

Solution:

Evaluate the following to 4 decimal places. 1) log 76 2) log 0. 43 … 1. 8808 3) ln 76 … – 0. 3665 4) ln 0. 43 … 4. 3307 5) log 56 … – 0. 8440 6) log. 76 … 1. 7482 … –. 1192

Intro to Logs Practice: Write the form given. Identify it as “Log Form” or “Exponential Form” and then convert it to the other form. 1) 5 x = 56 2) logx+1 (34) = 13 3) log 7 (3 x – 2) = 128 4) w(x – 3) = 6 y Use your calculator to evaluate the following log values to 4 decimal places. 5) log 54 6) log 0. 64 7) 8) log 1. 45 log 10 87 9) ln 78 10) ln 1. 26