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 can’t

just divide by 2—it’s not a coefcient, it’s a base—so you need to use

logarithms.

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