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The Humongous Book of Algebra Problems by W. Michael Kelley

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Chapter 18
LOGARITHMIC FUNCTIONS
In preceding chapters, the vast majority of the expressions that contained
exponential powers consisted of a variable raised to a real number expo-
nent, such as x
5
or y
2
. Solving equations containing such powers required a
radical with an index equal to the exponent to isolate x.
Functions containing variables in the exponent, such as 5
x
and 2
y
, are very
different than polynomials. Chapter 19 explores equations containing such
expressions, but to solve those equations, you must first understand the log-
arithmic function, which allows you to isolate the variable exponent.
To solve an equation like x
2
= 9, take the square root of both sides to
get x = ±3. Radicals allow you to isolate x by eliminating the attached
exponent.
This chapter deals with exponents that contain variables. If you want to
solve 2
x
= 9, you need a way to isolate x and get rid of the 2. You cant
just divide by 2—it’s not a coefcient, it’s a base—so you need to use
logarithms.
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