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

Name Date

WORKSHEET 8.20: SOLVING LOGARITHMIC EQUATIONS

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A logarithmic equation is an equation that contains a logarithmic expression. Solve

logarithmic equations by following the steps below:

1. Rewrite the equation in exponential form.


2. Solve the exponential equation.

EXAMPLES

log 2 x=5logx 216 =3log 381 =x

25 =xx^3 = 216 3 x=81; 81= 34

32 =xx= 216

1

(^3) orx= 63 x= 34 orx= 4
DIRECTIONS: Solve.

1. log 42 =x 2. log 5125 =x


2. log 82 =x 4. logx

1

7

=− 1

5. log 25 x=

1

2

6. log 6

1

36

=x

7. log 864 =x 8. log 16 x=−

1

2

9. logx 243 = 5 10. log 264 =x

CHALLENGE:Elena solved log 10010 =xand found thatx=2because

102 =100. Is she correct? Explain your reasoning.

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Copyright

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2011 by Judith A. Muschla, Gary Robert Muschla, and Erin Muschla. All rights reserved.