Solving Logarithmic Equations: Strategies and Examples
Explore strategies for solving logarithmic equations, including changing bases and using inverse properties. Practice with examples and learn to check for extraneous solutions. Enhance your skills in this essential topic.
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Presentation Transcript
WARM - UP Solve the following equation (for x) 8 36 ?= 40
SOLVING EXPONENTIAL & LOGARITHMIC FUNCTIONS SECTION 3.4
OBJECTIVES Students will be able to Solve logarithmic equations Solve equations with variables in the exponents Evaluate logs and natural logs Use the change of base formula to evaluate logs with bases other than 10
STRATEGIES FOR SOLVING EXPONENTIAL AND LOGARITHMIC FUNCTIONS Rewrite the original equation in a form that allows the use of the One-to-One Properties of exponential or logarithmic functions Rewrite an exponential equation in logarithmic form and apply the Inverse Property of logarithmic functions (log???= ? and ?log??= ?) Rewrite a logarithmic equation in exponential form and apply the Inverse Property of exponential functions. (ln??= ? and ?ln ?= ?)
EXAMPLES Solve each equation and approximate the result to three decimal places if necessary (exponentiating each side) 1) ln? = 3 2) ln? = 2
EXAMPLES 3) log35? 1 = log3(? + 7) 4) log63? + 14 log65 = log62?
EXAMPLES 5) 5 + 2ln? = 4 6) 2log53? = 4
CHECKING FOR EXTRANEOUS SOLUTIONS Solve: log5? + log ? 1 = 2
WHEN GRAPHING We can now solve for the x-intercept (instead of finding the 2ndpoint the way we were before) To find the x-intercept of our graph, set the function (y) equal to zero and solve for x. Example: Find the x-intercept of ? ? = log5? + 1 + 1
PRACTICE Work on worksheet 3.4 Solving Logarithmic Equations
HOMEWORK Finish 3.4 Solving Logarithmic Equations Worksheet
CLOSURE On the post it note provided, answer question #3 on your universal exit ticket (post on the board on way out the door)
