Exponential and Logarithmic Functions as Inverses

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.