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Exponential Equations: Example 14
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Properties of Exponents
Let
Solve
f
(
x
) = 2.
Let's review functional notation.
Does this require evaluation of
f
(2)?
No.
f
(
x
) = 2 requires finding a value of x which, when substituted in
f
(
x
), produces 2.
Does
f
(
x
) mean
f
multiplied by
x
?
No.
f
(
x
) is the name of the set of instructions represented by
.
So what do we work on?
f
(
x
) = 2 means to solve
How can we solve this?
By isolating
Do it.
Add 3 to both sides.
Should we now divide by 8 on both sides?
No, not until we take care of the exponent.
How can we clear the exponent?
By raising each side to the 3rd power.
Do it.
, or
8
x
= 125
Solve for
x
.
How can we check this result?
We can substitute it into the
original equation
.
Do that.
We get
, or
, or
5 – 3 ? 2, or
2 = 2
It checks!
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General Contents
Detailed Contents
Index