Exponential And Logarithmic Equations Worksheet With Answers
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1
2Solving Exponential and Logarithmic Equations
Exponential Equations (
variable in exponent position)
exp
onent
base
1. Isolate the exponential portion (
): Move all non-exponential factors or terms to the other side of
the equation.
2. Take ln or log of each side of the equation.
=
•
1
Make sure to use ln if the base is “e”. Then remember that ln e
.
•
Make sure to use log if the base is 10.
•
If the base is neither “e” nor “10”, use either ln or log, your choice..
3. Bring the power (exponent) down into coefficient position.
4. Use various algebra techniques to solve for the variable.
5. Check your answer by evaluating the original equation with your calculator.
−
=
2
x
3
Example:
4
e
40
Answer is on next page
Logarithmic Equations
1. Move all log terms to one side of the equation, all non-log terms to the other side.
2. Combine log terms into a single log term using the laws of logarithms.
=
↔
=
3
2
8
log
8
3
3. Write the log equation in its exponential form. (remember:
)
2
4. Use various algebra techniques to solve for the variable.
5. Check your answer using your calculator. Remember that domain problems occur in log functions.
•
If the base of the log is “10” or “e”, you can use the appropriate calculator keys.
•
If the log is not “10” or “e”, you may need to use the change of base formula before using your
calculator.
+
−
=
−
Example:
log
(
x
) 1
2
log
(
x
) 1
Answer is on next page
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