NAME:__________________________________________
DATE:____________
Algebra 2: Lesson 10 – 1 – An Introduction to Logarithms
Learning Goals
1. What is a logarithm?
2. How do we convert between logarithmic and exponential form?
Do Now: Find the inverse of each of the following.
1) ( )
2) ( ) √
3)
( )
What happens when you try to find the inverse of problem 3?
Defining Logarithmic Functions
The function
is the name we give the inverse of
A logarithm gives as its output (y-value) the exponent we must raise b to in order to produce its input (xvalue).
How would you write the inverse to problem 3 using some form of the word logarithm?
What are logarithms?
logbN = x means bx = N
(b > 0 and b ≠ 1)
Trick to remember:
Loop:
log N
b
bx = N
=x
#
Exponential Form
1
Logarithmic Form
log264 = x
2
logx81 = 4
3
log5x = 2
4
72 = x
5
x3 = 27
6
logbN = x
Part 1: Write each exponential equation in logarithmic form.
1) 24 = 16
1)
1
2) 8 3  2
2)
Part 2: Write each logarithmic equation in exponential form.
5
2
4)
1
 1
a
5)
3) log4 32 
4) loga
x
Part 3: Solve each equation for x:
5) log2x = 4
7) log6x = -2
Part 4: Evaluate each expression:
9) log25125
11) log49
1
7
6) log81x = ½
8) log64 x 
10) log5
1
25
12) log1000.1
2
3
Part 5: Solve each equation for b.
13) logb27 = 3
15) logb 5 
1
4
14) logb
1
 1
2
16) logb 4 
1
2
17) If f(x) = log3x, find f(1).
18) Verify the following by evaluating the logarithms:
( )
( )
(
)