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Exponential and Log Equations
An exponential or log equation is defined her as any equation that contains one or more
exponential or logarithmic terms.
We will use the property that allows us to take the log
of both sides of an equation shown immediately below. Also, in some cases we will solve
equations by doing what is often described as “unlogging” both sides of an equation,
also covered in this property.
Logarithms of Both Sides of an Equation
Given two positive quantities, U and V, and a legitimate base
a
,
If U = V, Then LOG
a
(U) = LOG
a
(V).
and likewise
If LOG
a
(U) = LOG
a
(V), then U = V.
Mathematically, we can write this as
U = V ifandonlyif LOG
a
(U) = LOG
a
(V)
.
Solving Exponential Equations:
To solve an equation containing exponential terms, use the following procedure:
1.
Isolate the exponential term on one side of the equal sign.
2.
Take the log function of both sides.
Use
base10 or basee logs and match the
base of your exponential if possible.
3.
Apply the Power Rule for Logs to move the exponent in front of the log.
4.
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 Fall '09
 Crandall
 Anthropology

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