The Algebra Teacher\'s Guide to Reteaching Essential Concepts and Skills

Teaching Notes 8.20: Solving Logarithmic Equations

To solve a logarithmic equation, students mustwrite the equation in exponential form. A

common mistake is failing to remember that the logarithm of a number is an exponent.

1. Explain that logarithmic equations can be rewritten as exponential equations. Depending
   on the abilities of your students, you may find it helpful to review 8.19: ‘‘Writing Logarith-
   mic Equations as Exponential Equations.’’ Emphasize that the logarithm of a number is the
   exponent. For example, log 6 x=2 can be rewritten as 6^2 =x.


2. Explain that once the exponential equation is written, the equation can be solved.


3. Review the information and examples on theworksheet with your students. Note that there
   are three types of equations: one in which a number is the base and a number is the exponent
   (as in the first example); another in which the base is a variable (as in the second example);
   and a third in which an exponent is a variable (as in the third example). The first equation
   is solved by evaluating the expression. To solve the second equation, students must ask
   themselves what number raised to the third power is 216. They may use guess and check
   to solve the equation or find the cube root of 216. To solve the third equation, students must
   rewrite the equation so that the bases are the same. They must then solve forx.

EXTRA HELP:

Double-check that the equation is written correctly before you try to solve it.

ANSWER KEY:

(1)x=

1

2

(2)x= 3 (3)x=

1

3

(4)x= 7 (5)x= 5

(6)x=− 2 (7)x= 2 (8)x=

1

4

(9)x= 3 (10)x= 6

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(Challenge)Elena is incorrect. She rewrote the equation incorrectly. It should be 100x=10,

thereforex=

1

2

.

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312 THE ALGEBRA TEACHER’S GUIDE