Exponential and Logarithmic Equations

Lesson 5.6

Solving Exponential Equations Graphically

Given Graphical Solution

Graph each side of the equation Use calculator to find intersection

0.1 10 0.5x

y = 0.5y = 0.5

y = 0.1 (10x)y = 0.1 (10x)

Solving Exponential Equations Symbolically

Given

Isolate the coefficientwith the exponent

Take log of bothsides

Use logarithm properties

Use division

0.05 1.15 5x

1.15 100x

log 1.15 log100 2x

log 1.15 2 x

2

log 1.15x

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

ln 4 1.5xe e

1.54x e

1.5

4

ex

Logarithmic Equation

Graphical solution of ln 4x = 1.5 As before graph both sides of the equation

y = ln 4x y = 1.5

Use calculatorto find intersection

Try It Out

Given

Part of class solve graphically

Part of class solve symbolically

2log 3 2 log 1x x Will they ever meet again?

Will they ever meet again?

2log 3 2 log 110 10x x

Now what?Now what?

Applications

Gambling revenues (in billions $) from 1991 to 1995 can be modeled by x is the year, x = 0 is 1991

When did revenues reach $45 billion?

0.131( ) 26.6 xf x e

Assignment

Lesson 5.6 Page 456 Exercises 1 – 57 EOO

73 – 93 EOO