1. Lesson 6.3 Logartithms and Logarithmic Functions(Day 1)
Learning Goal: (F.LE.A.4)
I can explain the relationship between exponents and logarithms.
I can evaluate logarithms by using the relationship with exponents.
Essential Question: What is the relationship between logarithms and exponents ?
Homework Discussion

2. Developed by John Napier in 1614 “for use in the extensive plane and 
spherical trigonometrical calculations necessary for astronomy”.
Word Origin: from two ancient Greek terms
logos meaning proportion
arithmos meaning number
Logarithms
In this course, we will be using the inverse relationship between 
exponential and logarithmic functions to solve problems.

3. The inverse of an exponential function is a logarithmic function.
Example:
f(x) = 2x
y = 2x (replace f(x) with y)
x = 2y (swap x and y)
______ = y (solve for y using definition of logs)
f-1(x) = _______ (use inverse notation)
Definition of Logarithm:
For all positive numbers b, where b ≠ 1, the
logby = x if and only if bx = y.
(logby ⇒ "the logarithm with base b of y" or "log base b of y")
Note: The _____ of the logarithm and the ______ of the 
exponent are the same. The logarithm _______ the exponent.
Are there any restrictions on the value of y? Justify your answer.

4. Rewriting Logarithmic Equations
logby = x if and only if bx = y
Rewrite each equation in exponential form.
a. log2 16 = b. log4 1 = 0
c. log12 12 = d. log1/4 4 = −1
Discussion on b and c
Logarithm of 1
Logarithm of b with Base b

5. Rewriting Exponential Functions
logby = x if and only if bx = y
Rewrite each equation in logarithmic form.
a. 52 = b. 10−1 = 0.1
c. 82/3 = d. 6−3 =
Your Turn

6. logby = x if and only if bx = y
Evaluating Logarithmic Expressions
logby = x if and only if bx = y
Evaluate each logarithm.
a. log b. log c. log1/ d. log36 6
Specific Logarithms
Common Logarithms: base 10 ; log x = log10x
Natural Logarithms: base e ; ln x = logex
Example: Evaluate using a calculator.
a. log b. ln0.3

7. Your Turn
Rewrite the equation in exponential form.
1. log3 81 = log7 7 = 1
3. log14 1 = log1/2 32 = −5
Rewrite the equation in logarithmic form.
5. 72 = = 1
7. 4−1 = /8 = 2

Evaluate the logarithm. If necessary, use a calculator and round your answer to three decimal places.
9. log log log ln 0.75

8. Practice to Strengthen Understanding
Exit Question:
What is the relationship between exponential functions and logarithmic functions?
Practice to Strengthen Understanding
Hmwk #4 BI p314 #5-25, (show work for #17-24)