8.1 ­ Logarithms (Solutions).notebook
Chapter 8
Logarithmic Equations
8.1 Understanding
Logarithms
October 28, 2015
8.1 ­ Logarithms (Solutions).notebook
October 28, 2015
A LOGARITHM is an exponent.
Logarithms are just another way to arrange information
involving bases and exponents.
Example:
Log5 25
Read as:
Means:
"log base 5 of 25"
"what exponent on 5 will give us
a result of 25?"
The answer: "is 2" b/c (5 2 = 25).
Log5 25 = 2
Example 1
Exponential Form
3 2= 9
Logarithmic Form
Log3 9 = 2
These two expressions are equivalent. They are simply
different ways to express the same information.
Example 2
Exponential Form
2 4 = 16
Logarithmic Form
Log2 16 = 4
8.1 ­ Logarithms (Solutions).notebook
October 28, 2015
Change the following from exponential form to logarithmic form.
Questions
Answers
Correct Answers
1. 2
4
= 16
1.__________________
1. log2 16 = 4
2. 4
5
= 1024
2.__________________
2. log4 1024 = 5
3. 7
3
= 343
3.__________________
3. log7 343 = 3
4. 6
2
= 36
4.__________________
4. log6 36 = 2
5. 5
3
= 125
5.__________________
5. log5 125 = 3
Change the following from logarithmic form to exponential form.
Questions
Answers
Correct Answers
1. log3 9 = 2
1.__________________
1. 32 = 9
2. log2 32 = 5
2.__________________
2. 25 = 32
3. log4 64 = 3
3.__________________
3. 43 = 64
4. log5 25 = 2
4.__________________
4. 52 = 25
5. log7 49 = 2
5.__________________
5. 72 = 49
8.1 ­ Logarithms (Solutions).notebook
October 28, 2015
Evaluating Logarithmic Equations
First change the equation into an exponential
equation. Then solve the exponential equation.
For example:
Solve for x: Log2 x = 3
Change to an exponential equation:
solve for x:
23 = x
x = 8
Evaluate the following logarithmic equations and expressions
log7 x = 2
log3 x = 4
log2 32
log7 x = 0
log5 125
8.1 ­ Logarithms (Solutions).notebook
Log this into your brain!
1. Page 98, #s 1­39 (odd)
2. Read example 5 on page 97
3. Page 99, #47, 50
October 28, 2015