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

Name Date

WORKSHEET 8.19: WRITING LOGARITHMIC EQUATIONS AS

EXPONENTIAL EQUATIONS

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A logarithmic equation of the formy=logbxcan be rewritten as an exponential equation of

the formx=by. Follow the steps below:

1. Usethelogarithmicequationtoidentifyy,b,andx. Remember thatbis always the base.


2. Substitute these values in the exponential equation,x=by.


3. Check your work.

EXAMPLES

2 =log 864 log 36216 =

3

2

y=2,b=8,x= 64 y=

3

2

,b=36,x= 216

x=by→ 64 = 82 x=by→ 216 = 36

3

2

8 · 8 = 64 36

1

(^2) =6, 6^3 = 216
DIRECTIONS: Write an exponential equation for each.

1. 3 =log 28 2.

1

2

=log 255 3. log 749 = 2

3

2

=log 1664 5. log 8

1

4

=−

2

3

CHALLENGE:Louis copied a logarithmic equation from the board incorrectly

as log√ 5 =5. The correct exponential equation is (

√

5)^2 =5. What is the

correct logarithmic equation?

311

Copyright

©

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