PreCalculus: Lesson Plan * 10/30/2006

Quickstart
p.254 #43 - 51

Assignment
Review #246
Solving exponential equations

Lesson
3.4 Solving Exponential and Logarithmic Equations
Objectives: Students will know how to solve exponential and logarithmic equations.

III. Solving Logarithmic Equations
There are two basic ways of solving logarihmic equations.
1. Isolate the logarithmic expression and then write the equation in equivalent exponential form.
2. Get a single logarithmic expression on each side of the equation, with the same base, then use the one-to-one property.

Example 2: Solve the following logarithmic equations and round your answer to three decimal places.
a) 2logx = 5
log x = 5/2
x = 10^5/2
x ≈ 316.228
b) ln √(x + 2) = ln x
e^{ln √(x + 2)} = e^{ln x}
√(x + 2) = x
x + 2 = x²
x² - x - 2 = 0
(x - 2)(x + 1) = 0
x - 2 = 0, x = 2
OR
x + 1 = 0, x = -1
-1 cannot be a solution because of the domain of the logarithmic function.
c) log x - log(x - 3) = 1
log [x/(x - 3)] = 1
x / (x - 3) = 10¹
x = 10(x - 3)
x = 10x - 30
-9x = -30
x = 10/3

Think-Pair-Share
p.255 #95, 97

IV. Approximating Solutions p.252
Some equations are beyond our algebraic skills and ony approximate solutions can be obtained.
See p.252 Example 11

Homework
p.254 - 256
#15 - 60 x 3's
#81 - 96 x 3's
#118

"Age affects how people experience time. The observations on this are well known, so it is only necessary to outline briefly what has been the experience of everyone I have ever talked to or read about: the years go faster as one gets older. At the age of four or six, a year seems interminable; at sixty, the years begin to blend and are frequently hard to separate from each other because they move so fast! There are, of course, a number of common-sense explanations for this sort of thing. If you have only lived five years, a year represents 20 percent of your life; if you have lived fifty years, that same year represents only 2 percent of your life, and since lives are lived as wholes, this logarithmic element would make it difficult to maintain the same perspective on the experience of a year’s passage throughout a lifetime." -Edward T. Hall, “Experiencing Time,” The Dance of Life: The Other Dimension of Time, Doubleday (1983)
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