Exponential and Logarithmic Equations Honors Precalculus November 1/2, 2016 Mr. Agnew

Essential Question Essential Vocabulary How do you solve logarithmic and exponential equations? Essential Vocabulary Exponential Equation Logarithmic Equation Laws of Logarithms Change of Base Formula

Change of Base Formula 𝒍𝒐𝒈 𝒃 𝑴= 𝒍𝒐𝒈𝑴 𝒍𝒐𝒈𝒃 Our calculators only understand the two special logarithms (common and natural) To evaluate logarithms with a base other than 10 or e on the calculator, we use the change of base formula: 𝒍𝒐𝒈 𝒃 𝑴= 𝒍𝒐𝒈𝑴 𝒍𝒐𝒈𝒃

Solving Exponential Equations An exponential equation is an equation in which the variable is in the exponent. How do we remove a variable from the exponent? 𝒚= 𝒃 𝒙 → 𝒍𝒐𝒈 𝒃 𝒚=𝒙 We rewrite it as a logarithm.

Solving Exponential Equations Steps to solve exponential equations: Isolate term that contains exponent Convert to logarithmic form Use change of base formula if necessary Solve for variable Examples

Logarithmic Equations A logarithmic equation is an equation in which the variable is “behind” the logarithm. 𝒍𝒐𝒈 𝒃 𝒚=𝒙→𝒚= 𝒃 𝒙 Remember how to rewrite from logarithmic to exponential form:

Logarithmic Equations Solving logarithmic equations: Combine all logarithmic expressions Isolate logarithm Rewrite in exponential form Solve for variable Examples…

Solving Equations Graphically How have we used the calculator to solve equations before? Set equation equal to zero, graph, and find zeros. Guided Practice

Homework: page 315 – 316 #11 – 25 (Odd), 26, 30, 31, 39, 49, 50