Introduction to Logarithmic Functions

INVERSES of Exponential
and Logarithmic Function

Content Standards:

AF:3: Apply the properties and key features of

logarithmic functions

AF.3.1: Execute properties of logarithms to rewrite expressions and solve equations algebraically.

​Learning Goal:
Rewrite logarithmic expression into exponential to solve equations algebraically.

Definition:

Logarithmic functions are the inverses of

exponential functions, and any exponential function

can be expressed in logarithmic form.

❖ Similarly, all logarithmic functions can be

rewritten in exponential form.

❖

Logarithms are

really useful in

permitting

us

to work with

very

large

numbers while

manipulating

numbers of a

much

more

manageable

size.

If x = 2 were to be solved for y, so that it could be written in
function form, a new word or symbol would need to be
introduced. If x = 2 , then y = (the power on base 2) to equal x.

The word logarithm, abbreviated log, is introduced to satisfy this
need.

y = (the power on base 2) to equal x

This equation is rewritten as y = log₂x.

This is read as “ y equals the log of x, base 2” or “ y equals the
log, base 2, of x.”

A logarithmic function is the inverse of an exponential function.

Multiple Choice

Rewrite log₂8 = 3 in exponential form.

• 2⁸ = 3

• 2³ = 8

• 3² = 8

• 8³ = 2

Multiple Choice

Rewrite the equation into log form.

• A

• B

• C

• D

Multiple Choice

Rewrite 3⁴ = 81 in logarithmic form.

• log₃4 = 81

• log₈₁ 4 = 3

• log₄ 3 = 81

• log₃ 81 = 4

Multiple Choice

Rewrite the log equation to its exponential form.

• A

• B

• C

• D

Multiple Choice

If it looks like there's no base under a log, there's an invisible ___ and this is called the _____________ log.

• 10, common

• 10, natural

• e, common

• e, natural

Multiple Choice

The common logarithm has what base?

• 10
• 0
• e
• -e

Multiple Choice

Rewrite log₂8 = 3 in exponential form.

• 2⁸ = 3
• 2³ = 8
• 3² = 8
• 8³ = 2

Multiple Choice

Change to Exponential Form:
log₆36 = 2

• 2⁶=36
• 6²=36
• 36²=6
• 36⁶=2

Multiple Choice

Rewrite log_pt = m in exponential form.

• p^t = m
• t^m = p
• m^t = p
• p^m = t

Multiple Choice

log₄1 = 

• 0
• 1
• 4
• DNE

Multiple Choice

Evaluate:
log₄16

• 2
• 4
• 1/2
• -2