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5.7 – Exponential Equations

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5.7 Exponential Equations Objectives: I will be able to… Solve Exponential Equations using the Change of Base Formula Vocabulary: logarithms, natural logarithms

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Daily Objectives Perform the Change of Base formula. Master solving tricky logarithm equations. ▫Exponent variables

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Topic One: Change of Base Formula The BASE goes to the BOTTOM We typically use log base 10 so we can solve on our calculator!

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Example 1: Using Change of Base Formula This is a great problems to use the change of base formula on – Why? On the other hand, why is problem #2 not the type of problem that you should use the change of base formula on? #3 can work with either – Why?

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Example 2: Using Change of Base Formula

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Example 1: Solve for a variable exponent when you can have same base

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Example 2: Solve for a variable exponent when it’s impossible to get same base 1.Get the base/exponent by itself on one side of the equation (use PEMDAS) 2.Take the log of both sides 3.Bring down the exponent via the Log Power Rule 4.Get x by itself using Change of Base Rule! 5.**Remember: ln(e)=1 and log(10)=1

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Example 3: Solve for a variable exponent

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Example 4: Solve for a variable exponent

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Example 5: Solve for a variable exponent

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Example 6: Solve for a variable exponent

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Going back to Growth/Decay….

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Now you solve for time!

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Homework p. 205 #5-14

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