Solving Exponential Equations,
where
x
is in the exponent, BUT
the bases DO NOT MATCH.
Step 1:
Isolate the exponential expression.
Get your exponential expression on one side everything outside of the
exponential expression on the other side of your equation.
Step 2:
Take the natural log of both sides.
The inverse operation of an exponential expression is a log. Make sure that
you do the same thing to both sides of your equation to keep them equal to
each other.
Step 3:
Use the properties of logs to pull the
x
out of the exponent.
If you need a review on log properties, feel free to go to
Tutorial 44:
Logarithmic Properties
. I think you are ready to get started.
Step 4:
Solve for
x
.
Now that the variable is out of the exponent, solve for the variable using
inverse operations to complete the problem.
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View Full DocumentSpecial Note:
The only way we can get that variable out of the exponent, when the bases don't match
up, is to use logs. The 3rd step allows us to do this. When solving an equation, it
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 Spring '11
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 Algebra, Exponential Function, Equations, Taylor Series, Exponentiation, Logarithm, exponential expression, lne

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