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

(Marvins-Underground-K-12) #1

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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