Inverse with Exponential Functions

Logarithmic Function

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.

Ifx = 2 ywere 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 y, 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 = log 2x.

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

Rewrite each exponential equation in its equivalent logarithmic form.

The solutions follow.

Multiple Choice

Express exponential into logarithmic form.

• log216 (3) = 6

• log6 (216) = 3

• log3 (216) = 6

• log216 (6) = 3

Fill in the Blanks

Multiple Choice

Express exponential into logarithmic form.

• log36 (6) = 1/2

• log6 (1/2) = 36

• log36 (1/2) = 6

• log1/2 (6) = 36

Multiple Choice

Express logarithm into exponential form.

• 27^3 = 3

• 3^27 = 3

• 3^3 = 27

• 3^9 = 27

Fill in the Blanks

Multiple Choice

• 2^2 =3

• 8^2 = 2

• 2^1/3 = 8

• 8^1/3 =2

Open Ended

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