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:
- Usethelogarithmicequationtoidentifyy,b,andx. Remember thatbis always the base.
- Substitute these values in the exponential equation,x=by.
- 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.
- 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.