Aim: How do we solve exponential equations using logarithms?

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Aim How do we solve exponential equations
using logarithms?

• Do Now

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Solving Exponential Equations
What is an exponential equation?
An exponential equation is an equation, in which
the variable is an exponent. Ex.
3x - 4 9
Question What power of 3 will give us 9?
Answer 2
? x - 4 2
and x 6
Solution of this equation was possible because 9
is a power of 3 or in general terms For b gt 0,
and b ? 1, bx by ? x y
To solve an exponential equation, write each side
as a power of the same base.
3x - 4 32
rewrite each side with same base
x - 4 2
equate the exponents and solve
x 6
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Exponential Equation Problems
Solve and check 5x 1 54
Solve and check 2x - 1 82
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Exponential Equation Problems
Solve and check 9x 1 27x
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Exponential Equation Problems
Solve and check
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Solving Exponential Equations w/Logs
What if the two sides of the exponential equation
cannot be expressed with the same base? Ex. 9x
14
log 9x log 14
x log 9 log 14
91.202 14
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Alternate Method - 1
Solve for x to the nearest 10th 12 12x 500
Method 1
log (12 12x) log 500
log 12 log 12x log 500
log 12 x log 12 log 500
x log 12 log 500 - log 12
x 1.5 to nearest 10th
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Alternate Method - 2
Solve for x to the nearest 10th 12 12x 500
Method 2
1.5
9
Alternate Method - 3
Solve for x to the nearest 10th 12 12x 500
Method 3
121 x 500
log 121 x log 500
(1 x)log 12 log 500
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Problems
Solve 6x 42 to 3 decimal places
Solve 3.1a 3 9.42 to 3 decimal places
a 4.982
Solve 9a 2a
a 0
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Complicated Problem
Solve 82x - 5 5x 1
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Problems
Solve 4e2x 5 to 3 decimal places
Check 4e2(0.112) 5