5.5 Logarithms

5.5 Logarithms

Objectives: I will be able to… Rewrite equations between exponential and

logarithmic forms Evaluate logarithms Solve logarithms

Vocabulary: logarithms, natural logarithms

Why learn about logarithms?

•5.1-5.4 were all about exponents•A logarithm is the inverse of an

exponent•We can use logarithms to solve for a

missing exponential value

Two special types of logarithms:

Logarithmic Function

• Common Log No b means base 10

• Natural Log ln means base e

Logarithmic Function

x and b are ALWAYS POSITIVEy can be + or -

We discovered last week that exponential functions followed the same translation rules as polynomials.We can switch between these two forms to assist us in solving problems.

base

number

exponent

Rewrite Exponents Logs⟶

b = 6

x = 216

b = 10

x = .01

b= e

x = .0498

𝐥𝐨𝐠𝟔𝟐𝟏𝟔=𝟑

𝐥𝐨𝐠 .𝟎𝟏=−𝟐

𝐥𝐧 .𝟎𝟒𝟗𝟖≈−𝟑

Solve for the missing variable by changing to exponential form.log5 c = 3 loga64 = 2 log7 = w

Logarithmic Function

c 125 c

64 a ± 8

w -2

Evaluate:

Logarithmic Function

Evaluate:

If not an equation, let log equal y as in general form.=y

No base means base 10.

.01 -2

6 𝑦=612

y

10𝑦=−1000

Remember number and base can not be negative.

𝑒𝑦=𝑒25y

=y =y =y10 e

Solve for x using logarithm and exponent rules.

Logarithmic Function

Change form of logarithm.

Change form of 729.

Use exponent rules.Not matching exponents, must get rid of exponent with x.

p. 194-195 #11, 12, 14, 17, 36-42 evenHomework

Exit Ticket

1. Rewrite the following log functions into exponential form:a)

b)

2. Solve for x.a)

b)