8.6 Solving Exponential & Logarithmic Equations

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Presentation transcript:

8.6 Solving Exponential & Logarithmic Equations Standards 13, 14 8.6 Solving Exponential & Logarithmic Equations

Solve by Equating Exponents Original Problem Rewrite with base 2 Simplify exponents Equate exponents Simplify Goal 1: Solving Exponential Functions

Goal 1: Solving Exponential Functions White Boards a. b. Goal 1: Solving Exponential Functions

Taking the Log of both sides Original Problem Take log2 of each side Simplify Change-of-base formula Goal 1: Solving Exponential Functions

Goal 1: Solving Exponential Functions White Boards a. b. Goal 1: Solving Exponential Functions

Goal 1: Solving Exponential Functions More complicated... Solve by taking the log of both sides. Original Problem -4 from both sides log both sides Simplify +3 ÷2; Simplify Goal 1: Solving Exponential Functions

Goal 1: Solving Exponential Functions White Boards Solve by taking the log of both sides. Goal 1: Solving Exponential Functions

Goal 2: Solving Logarithmic Functions Solving Log Equations Original Problem Same bases cancel Isolate x Goal 2: Solving Logarithmic Functions

Goal 2: Solving Logarithmic Functions White Boards Goal 2: Solving Logarithmic Functions

Goal 2: Solving Logarithmic Functions Exponentiating... Original Problem Exponentiate both sides Simplify Isolate x Goal 2: Solving Logarithmic Functions

Goal 2: Solving Logarithmic Functions White Boards a. b. Goal 2: Solving Logarithmic Functions

Goal 2: Solving Logarithmic Functions Extraneous Solutions Goal 2: Solving Logarithmic Functions

Goal 2: Solving Logarithmic Functions Solving Log Equations Goal 2: Solving Logarithmic Functions