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Understanding Exponential Equations and Logarithmic Inverses

In this lesson, we explore exponential equations of the form y = ab^(x-h) + k, focusing on the process of solving for x when given y values. Students will practice raising 2 and 3 to various powers to find x. Additionally, we will learn about logarithms and finding inverses by applying a four-step method: replace f(x) with y, switch x and y, solve for y, and replace y with f⁻¹(x). This foundational knowledge will enhance students' understanding of exponential and logarithmic functions.

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Understanding Exponential Equations and Logarithmic Inverses

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  1. Bellwork: Get a sheet from the front desk and completeTurn in the assignment from last class if you have not already

  2. Recall: These are equations of the form y=abx-h+k, ones where the ‘x’ is in the exponent Exponential Equations

  3. x = the power you raise 2 to in order to get 8 x = the power you raise 2 to in order to get 5 x = the power you raise 2 to in order to get 4 y=2x

  4. x = the power you raise 3 to in order to get 9 x = the power you raise 3 to in order to get 4 x = the power you raise 3 to in order to get 1 y=3x

  5. x = the power you raise 2 to in order to get 5 x = the power you raise 3 to in order to get 4 Logarithms!

  6. Let’s find some inverses EX1: STEP 1: Replace f(x) with y. STEP 2: Switch x and y. STEP 3: Solve for y. STEP 4: Replace y with f-1(x)

  7. Let’s find some inverses EX2: STEP 1: Replace f(x) with y. STEP 2: Switch x and y. STEP 3: Solve for y. +1 +1 STEP 4: Replace y with f-1(x)

  8. Let’s find some inverses EX3: STEP 1: Replace f(x) with y. STEP 2: Switch x and y. STEP 3: Solve for y. -3 -3 STEP 4: Replace y with f-1(x)

  9. Let’s find some inverses EX4: STEP 1: Replace f(x) with y. STEP 2: Switch x and y. STEP 3: Solve for y. +4 +4 -1 -1 ÷3 ÷3 STEP 4: Replace y with f-1(x)

  10. Intro to Logs: In Class Practice (Assignment)

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