Introduction To Logarithms

Views:
 
Category: Education
     
 

Presentation Description

Introduction To Logarithms

Comments

Presentation Transcript

Introduction To Logarithms:

Introduction To Logarithms

Slide 2:

Our first question then must be: What is a logarithm ?

Slide 3:

Definition of Logarithm Suppose b>0 and b≠1, there is a number ‘p’ such that:

Slide 4:

You must be able to convert an exponential equation into logarithmic form and vice versa. So let’s get a lot of practice with this !

Slide 5:

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

Slide 6:

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

Slide 7:

Example 1b: Solution:

Slide 8:

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

Slide 9:

Solution:

Slide 10:

Solution:

Slide 11:

Solution:

Slide 12:

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.

Slide 13:

Example 1: Solution:

Slide 14:

Example 2: Solution:

Slide 15:

Okay, now you try these next three.

Slide 16:

Solution:

Slide 17:

Solution:

Slide 18:

When working with logarithms, if ever you get “stuck”, try rewriting the problem in exponential form. Conversely, when working with exponential expressions, if ever you get “stuck”, try rewriting the problem in logarithmic form.

Slide 19:

Solution: Let’s rewrite the problem in exponential form. We’re finished ! Example 1

Slide 20:

Solution: Rewrite the problem in exponential form. Example 2

Slide 21:

Example 3 Try setting this up like this: Solution: Now rewrite in exponential form.

Properties of logarithms:

Properties of logarithms

Slide 23:

Let b, u, and v be positive numbers such that b ≠1. Product property: log b uv = log b u + log b v Quotient property: log b u/v = log b u – log b v Power property: log b u n = n log b u

Expanding Logarithms:

Expanding Logarithms You can use the properties to expand logarithms. log 2 7x 3 / y= log 2 7x 3 - log 2 y = log 2 7 + log 2 x 3 – log 2 y = log 2 7 + 3 · log 2 x – log 2 y

Slide 25:

Expand: log 5mn = log 5 + log m + log n Expand: log 5 8x 3 = log 5 8 + 3 · log 5 x

Condensing Logarithms:

Condensing Logarithms log 6 + 2 log2 – log 3 = log 6 + log 2 2 – log 3 = log (6 ·2 2 ) – log 3 = log 24 – log 3= log 24/3= log 8

Slide 27:

Condense: log 5 7 + 3 · log 5 t = log 5 7t 3 Condense: 3log 2 x – (log 2 4 + log 2 y)= log 2 x 3 /4y

Change of base formula::

Change of base formula: u, b, and c are positive numbers with b ≠1 and c≠1. Then: log c u = log u / log c (base 10)

Examples::

Examples: Use the change of base to evaluate: log 3 7 = log 7 ≈ 1.771 log 3

authorStream Live Help