Algebra 3
Warm-Up 5.3
Solve each equation for x.
1.
3x – 12 = 45
x = 19
2.
5x  14
x = 39.2
Algebra 3
Lesson 5.3
Objective: SSBAT write and evaluate logarithmic
expressions.
Standards: 2.1.11A
Review:
Addition and Subtraction are opposite operations.
Multiplication and Division are opposite operations.
Squaring and Square Rooting are opposite operations.
Solve for x.
3x = 19683
 You could use guess and check or you can
use logarithms.
 Logarithms are the opposite of Exponential
functions.
Logarithmic Equation
 An equation of the form x = logb y
 y is a positive number
 Used to solve exponential equations
 logb y is read as “log base b of y”
Exponential Form To Logarithmic Form
y = bx
x = logb y
** The base of the Exponent becomes the base of
the Logarithm.
** The exponent is all by itself in the logarithm.
Write each in Logarithmic Form
1.
53 = 125
3 = log5 125
2.
45 = 1024
5 = log4 1024
3.
7m = 2401
m = log7 2401
4.
20736 = 124
4 = log12 20736
5.
100 = 1
3
6.
1 1
  
2 8
0 = log10 1
1
3  log 1  
2 8
Change each to Exponential Form
1.
log5 15625 = 6
56 = 15625
2.
log2 128 = 7
27 = 128
Change each to Exponential Form
3.
logx 2048 = 5.5
x5.5 = 2048
4.
log16
16

1
1
 2
4
1
4
=½
Common Logarithm
 A logarithm that has a base of 10
 log10 y
 You can write it as log y
- When there is no base shown it is base 10
 log10 15 = log 15
 Common Logarithms are used to measure pH (acidity),
decibels (sound), Richter Scale (earthquakes)
Since the Common Logarithm log10 is used the most in
real world applications it is given a key on the
calculator.
Evaluate each.
1.
log10 150
=
2.176
2.
log 240
=
2.380
3.
log -13
Undefined
Change of Base Property
 Used to evaluate non base 10 logarithms in your
calculator.
 For any positive number M and b, with b ≠ 1
logb M =
log M
log b
Evaluate log2 32
log (32)
log (2)
= 5
Evaluate each.
1.
log8 16

log (16)
log (8)
= 4/3 or 1.333…
2.
log9 27

log (27)
log (9)
3.
1
log 64  
 32 
 1 
log  
 32 

log (64)
= 1.5
= -.83333
4.
log4 (-600)
log (-600)

log (4)
Answer: Undefined
(cannot take the log of a negative number)
On Your Own.
1. Change to Logarithmic Form

54  625
4  log 5 625
2. Change to Exponential Form
log81 3 = ¼

811/4 = 3
3. Evaluate. Show the change of base form.
log2 8

log (8)
 3
log (2)
Homework
Worksheet 5.2