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## Logarithmic and Exponential Equations

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**CHECK! to make sure your answer is “legal”**Solve for the variable. If x is in more than one term get x terms on one side and factor out the x Re-write the log equation in exponential form If the log is in more than one term, use log properties to condense Steps for Solving a Logarithmic Equation**Re-write the log equation in exponential form**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**Solve for the variable. If x is in more than one term get x**terms on one side and factor out the x Re-write the log equation in exponential form If the log is in more than one term, use log properties to condense**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**Solve for the variable. If x is in more than one term get x**terms on one side and factor out the x Use the 3rd Property of Logs to move the exponent out in front If you have au= bv and you can’t express a and b with the same base, take the log of both sides(ln or log) Steps for Solving an Exponential Equation**Solve for the variable. If x is in more than one term get x**terms on one side and factor out the x Use the 3rd Property of Logs to move the exponent out in front If you have au= bv and you can’t express a and b with the same base, take the log of both sides(ln or log)**Solve for the variable. If x is in more than one term get x**terms on one side and factor out the x 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**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