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Logarithmic Equations

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This guide explores the creation and graphing of logarithmic equations, focusing on functions in the form f(x) = logb(x - h) + k. Learn how to graph logarithmic functions using the parameters h and k to build tables of values. Discover the process of solving equations where f(x) equals zero or a constant, like 3. The guide also discusses changing bases and their implications on function behavior, as well as comparing and contrasting exponential and logarithmic functions. Ideal for students and educators alike!

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Logarithmic Equations

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  1. Logarithmic Equations

  2. Create a Logarithmic Equation • Create a logarithmic function of the form • f(x) = logb (x-h) + k

  3. Graphing • Graph the Logarithmic Function Remember the base matters Use h and k to help build a table of values

  4. Create an Equation • Set f(x) = 0 and solve • F(x) = logb(x-h) + k • 0= logb (x-h) + k

  5. Change the value of F(X) • Now set f(x) = 3 • Solve new equation

  6. Change the Base • Change to a new base And solve for f(x) = 0

  7. Last STEP • Compare and Contrast Exponential and Logarithmic Functions

  8. Finished Product • Make Logarithmic Equation • Graph it • Solve for F(x) = 0 • Solve for F(x) = 3 • Change to a new base and solve for F(x) = 0 • Compare and Contrast Exponential and Logarithmic • Bonus: Compare the two bases what would that do to the graph

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