# Download Lesson 5.6

Survey
Was this document useful for you?
Thank you for your participation!

* Your assessment is very important for improving the work of artificial intelligence, which forms the content of this project

Document related concepts

Cubic function wikipedia, lookup

Quartic function wikipedia, lookup

Quadratic equation wikipedia, lookup

Elementary algebra wikipedia, lookup

Signal-flow graph wikipedia, lookup

System of polynomial equations wikipedia, lookup

History of algebra wikipedia, lookup

System of linear equations wikipedia, lookup

Equation wikipedia, lookup

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
```