Transcript Exponential and Logarithmic Equations

Exponential and
Logarithmic Equations
Lesson 5.6
Solving Exponential Equations
Graphically
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0.110 x   0.5
Given
Graphical Solution
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Graph each side of the equation
Use calculator to find intersection
y = 0.1 (10x)
y = 0.5
Solving Exponential Equations
Symbolically
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Given
0.05 1.15   5
x
Isolate the coefficient 1.15   100
with the exponent
x
Take log of both
log 1.15  log100  2
sides
x
 log 1.15  2
Use logarithm properties
x
Use division
2
x
log 1.15
Try It Out
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Given 3(2 x – 2) = 99
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Part of class solve graphically
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Part of class solve symbolically
Logarithmic Equation
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Consider ln 4x = 1.5
Symbolic solution
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Raise to the power of the base
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Use property of logarithms
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Use Division
e1.5
x
4
eln 4 x  e1.5
4x  e1.5
Logarithmic Equation
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Graphical solution of
ln 4x = 1.5
As before graph both sides of the equation
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y = ln 4x
y = 1.5
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Use calculator
to find intersection
Try It Out
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Given
log  x 2  3  2  log  x  1
Will they ever
meet again?
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Part of class solve graphically
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Part of class solve symbolically

10
log x 2 3
  102log x 1
Now what?
Applications
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Gambling revenues (in billions $) from 1991 to
0.131x
1995 can be modeled by f ( x)  26.6e
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x is the year, x = 0 is 1991
When did revenues reach $45 billion?
Assignment
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Lesson 5.6
Page 456
Exercises 1 – 57 EOO
73 – 93 EOO