Logarithmic and Exponential Equations

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Logarithmic and Exponential Equations
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Steps for Solving a Logarithmic Equation
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use the first property of logs to condense
under one log
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Remember that the domain of logs is numbers
greater than 0 so we need to make sure that if we
put our answers back in for x we wont be trying
to take the log of 0 or a negative number.
not illegal since first log is of 4 and second
is of 1
ah oh---cant take the log of - 1 or - 4 so must
throw this solution out
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Steps for Solving an Exponential Equation
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put in calculator making sure to enclose the
numerator in parenthesis and the denominator in
parenthesis
Solve for the variable. If x is in more than one
term get x terms on one side and factor out the x
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If you have an exponential equation with a base
e then isolate the e meaning get rid of other
terms and coefficients and then take the ln of
both sides. Remember that es and lns are
inverses and undo each other so theyll cancel
out and you can solve from there.
isolate the e
take the ln of both sides
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Acknowledgement I wish to thank Shawna Haider
from Salt Lake Community College, Utah USA for
her hard work in creating this PowerPoint. www.sl
cc.edu Shawna has kindly given permission for
this resource to be downloaded from
www.mathxtc.com and for it to be modified to suit
the Western Australian Mathematics Curriculum.
Stephen Corcoran Head of Mathematics St
Stephens School Carramar www.ststephens.wa.edu.
au