1. Logarithmic and Exponential Equations

2. Steps for Solving a Logarithmic Equation If the log is in more than one term, use log properties to condense Re-write the log equation in exponential form Solve for the variable. If x is in more than one term get x terms on one side and factor out the x CHECK! to make sure your answer is “legal”

3. If the log is in more than one term, use log properties to condense use the first property of logs to “condense” under one log Re-write the log equation in exponential form

4. If the log is in more than one term, use log properties to condense Re-write the log equation in exponential form Solve for the variable. If x is in more than one term get x terms on one side and factor out the x

5. CHECK! to make sure your answer is “legal” 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 won’t 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---can’t take the log of - 1 or - 4 so must throw this solution out

6. Steps for Solving an Exponential Equation If you have a u = b v and you can’t express a and b with the same base, take the log of both sides (ln or log) Use the 3rd Property of Logs to move the exponent out in front Solve for the variable. If x is in more than one term get x terms on one side and factor out the x

7. If you have a u = b v and you can’t express a and b with the same base, take the log of both sides (ln or log) Use the 3rd Property of Logs to move the exponent out in front Solve for the variable. If x is in more than one term get x terms on one side and factor out the x

8. put in calculator making sure to enclose the numerator in parenthesis and the denominator in parenthesis

9. 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 e’s and ln’s are inverses and “undo” each other so they’ll cancel out and you can solve from there. isolate the “e” take the ln of both sides.644

10. Acknowledgement I wish to thank Shawna Haider from Salt Lake Community College, Utah USA for her hard work in creating this PowerPoint. www.slcc.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.www.mathxtc.com Stephen Corcoran Head of Mathematics St Stephen’s School – Carramar www.ststephens.wa.edu.au