3.4 – Exponential and Logarithmic Equations
Pre-Calculus
Mr. Niedert
Pre-Calculus
3.4 – Exponential and Logarithmic Equations
Mr. Niedert
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3.4 – Exponential and Logarithmic Equations
1
Solving Simple Equations
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3.4 – Exponential and Logarithmic Equations
Mr. Niedert
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3.4 – Exponential and Logarithmic Equations
1
Solving Simple Equations
2
Solving Exponential Equations
Pre-Calculus
3.4 – Exponential and Logarithmic Equations
Mr. Niedert
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3.4 – Exponential and Logarithmic Equations
1
Solving Simple Equations
2
Solving Exponential Equations
3
Solving Logarithmic Equations
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3.4 – Exponential and Logarithmic Equations
Mr. Niedert
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Today’s Learning Target(s)
1
I can solve exponential equations.
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3.4 – Exponential and Logarithmic Equations
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Solving Simple Equations
You may need to review the following properties as you try to work
through the practice problem below.
One-to-One Properties
= ay if and only if x = y
loga x = loga y if and only if x = y
ax
Inverse Properties
aloga x = x
loga ax = x
Practice
Solve the following equations without a calculator.
a 2x = 32
b ln x − ln 3 = 0
x
c 13 = 9
d ex = 7
e ln x = −3
f log x = −1
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3.4 – Exponential and Logarithmic Equations
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Solving Exponential Equations
Example
Solve each equation and approximate the result to three decimal places if
necessary.
2
a e −x = e −3x−4
b 3 (2x ) = 42
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Exact and Approximate Solutions
In (b) of the previous example we found an approximate solution of
about 3.807.
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3.4 – Exponential and Logarithmic Equations
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Exact and Approximate Solutions
In (b) of the previous example we found an approximate solution of
about 3.807.
If you were to find the exact solution then the exact solution is
log2 14.
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Exact and Approximate Solutions
In (b) of the previous example we found an approximate solution of
about 3.807.
If you were to find the exact solution then the exact solution is
log2 14.
An exact solution is preferred when the solution is an intermediate
step in a larger problem. For a final answer, an approximate solution
is easier to comprehend.
Pre-Calculus
3.4 – Exponential and Logarithmic Equations
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Solving Exponential Equations
Practice
Solve each equation and approximate the result to three decimal places if
necessary.
2
a e −x = e 5x+6
b 4 (3x ) = 64
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3.4 – Exponential and Logarithmic Equations
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Solving Exponential Equations
Practice
Solve e x + 5 = 60 and approximate the result to three decimal places.
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3.4 – Exponential and Logarithmic Equations
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Solving Exponential Equations
Practice
Solve 2 32t−5 − 4 = 11 and approximate the result to the nearest
thousandth.
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3.4 – Exponential and Logarithmic Equations (Part 1 of 2)
Assignment
Part 1: pg. 253-254 #1-4, 10-20 even, 26-54 EOE
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Today’s Learning Target(s)
1
I can solve logarithmic equations.
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3.4 – Exponential and Logarithmic Equations
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Extraneous Solutions
When solving logarithmic equations, be sure to check your solution in
the original equation.
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Extraneous Solutions
When solving logarithmic equations, be sure to check your solution in
the original equation.
We will need to make sure that the results do not yield extraneous
solutions.
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Extraneous Solutions
When solving logarithmic equations, be sure to check your solution in
the original equation.
We will need to make sure that the results do not yield extraneous
solutions.
Remember that if you end up with extraneous solutions, they are not
considered to actually be solutions to the equation.
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3.4 – Exponential and Logarithmic Equations
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Solving Logarithmic Equations
Example
Solve ln x = 2.
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Solving Logarithmic Equations
Practice
Solve each equation.
a ln x =
2
3
b log4 (3x + 2) = log4 (6 − x)
c log3 (5x + 13) − log3 6 = log3 3x
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Solving Logarithmic Equations
Practice
Solve 5 + 2 ln x = 4 and approximate the result to three decimal places.
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3.4 – Exponential and Logarithmic Equations
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Solving Logarithmic Equations
Practice
Solve 2 log5 3x = 4.
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Solving Logarithmic Equations
Practice
Solve log 5x + log(x − 1) = 2.
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3.4 – Exponential and Logarithmic Equations (Part 2 of 2)
Assignment
Part 1: pg. 253-254 #1-4, 10-20 even, 26-54 EOE
Part 2: pg. 253-254 #5-8, 76-100 EOE
3.4 – Exponential and Logarithmic Equations Assignment
pg. 253-254 #1-8, 10-20 even, 26-54 EOE, 76-100 EOE
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