Logs - Day 1 TUESDAY, FEBRUARY 2, 2016 DEFINE THE TERMS ON PAGE 291 INTO YOUR VOCAB LIST! ADAPTED FROM: ODUCING-LOGARITHMS-WITH-FOLDABLES.HTML

Essential Question How do I convert an exponential equation to a logarithmic equation and vice versa? How do I evaluate common logs and natural logs with the calculator?

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 ”

base exponent = answer log base answer = exponent Exponential Form Logarithmic Form

Anytime the base of a logarithm is not written, it is assumed to be the number 10. E The logarithm answers the question: What power do I raise the base to in order to get _____?

The Logarithm Loop Trick (for changing forms) Always draw your loop counter-clockwise from the base!

Let’s Practice! HINTS: 1) THE BASE OF THE LOGARITHMIC FORM IS ALSO THE BASE OF THE EXPONENTIAL FORM… 2) REMEMBER, A LOGARITHM IS ALWAYS EQUAL TO THE POWER OF THE BASE TO GET THAT NUMBER!

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

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

Example 1b: Solution: 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!!

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

Solution: This brings up a special property of logarithms. Since anything to the power of 0 gives us 1, what will the log (base anything) of 1 always give us? log x 1 = 0

Solution:

Do you remember what a half-power represents? A half-power is a SQUARE ROOT.

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. 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:

Evaluating logarithms HINTS: 1) USE THE LOG BUTTON (BASE 10) OR THE LN BUTTON (BASE “E”) DEPENDING ON THE BASE. 2) FOR OTHER BASES, YOU WILL NEED TO KNOW THE “CHANGE-OF-BASE” FORMULA WHICH WE WILL LEARN LATER.

Evaluate the following to 4 decimal places. 1)log 762) log 0.43 … … – ) ln 764) ln 0.43 … … – )log 566) log.76 … … –.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) log x+1 (34) = 13 3) log 7 (3x – 2) = 128 4) w (x – 3) = 6y Use your calculator to evaluate the following log values to 4 decimal places. 5) log 546) log )log ) log ) ln 7810) ln 1.26

Intro to Logs Practice: KEY 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) log x+1 (34) = 13 3) log 7 (3x – 2) = 128 4) w (x – 3) = 6y Use your calculator to evaluate the following log values to 4 decimal places. 5) log 546) log )log ) log ) ln 7810) ln 1.26 log 5 (56) = x(x + 1) 13 = = 3x – 2log w (6y) = x – – points per problem. Put a grade on it! Title the page “Converting Logs”