Solve each equation for x.

1. 3x – 12 = 45

x = 19

2. 14 5 x

x = 39.2

Algebra 3

Warm-Up 5.3

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.

1. 53 = 125

Write each in Logarithmic Form

3 = log5 125

2. 45 = 1024 5 = log4 1024

3. 7m = 2401 m = log7 2401

4. 20736 = 124 4 = log12 20736

5. 100 = 1 0 = log10 1

6.8

1

2

13

8

1 log 3

2

1

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.

4

1-

2

1 log16

16 4

1

= 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. log 240

3. log -13

= 2.176

= 2.380

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 =

b log

M log

Evaluate log2 32

log (32)

log (2) = 5

Evaluate each.

1. log8 16

)8( log

)16( log

= 4/3 or 1.333…

2. log9 27

)9( log

)27( log

= 1.5

3.

32

1 log

64

(64) log321

log

= -.83333

4. log4 (-600)

(4) log

(-600) log

Answer: Undefined

(cannot take the log of a negative number)

On Your Own.

1. Change to Logarithmic Form

2. Change to Exponential Form

3. Evaluate. Show the change of base form.

62554 625 log 4 5

log81 3 = ¼ 811/4 = 3

log2 8 3 (2) log

(8) log

Homework

Worksheet 5.2