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Transcript
Exponential and
Logarithmic Equations
Lesson 5.6
Solving Exponential Equations
Graphically


0.110 x   0.5
Given
Graphical Solution


Graph each side of the equation
Use calculator to find intersection
y = 0.1 (10x)
y = 0.5
Solving Exponential Equations
Symbolically





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

Given 3(2 x – 2) = 99

Part of class solve graphically

Part of class solve symbolically
Logarithmic Equation


Consider ln 4x = 1.5
Symbolic solution

Raise to the power of the base

Use property of logarithms

Use Division
e1.5
x
4
e ln 4 x  e1.5
4x  e1.5
Logarithmic Equation


Graphical solution of
ln 4x = 1.5
As before graph both sides of the equation

y = ln 4x
y = 1.5

Use calculator
to find intersection
Try It Out

Given
log  x 2  3  2  log  x  1
Will they ever
meet again?

Part of class solve graphically

Part of class solve symbolically

10
  102log x1
log x2 3
Now what?
Applications

Gambling revenues (in billions $) from 1991 to
0.131x
1995 can be modeled by f ( x)  26.6e


x is the year, x = 0 is 1991
When did revenues reach $45 billion?
Assignment



Lesson 5.6
Page 456
Exercises 1 – 57 EOO
73 – 93 EOO