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Section 6.3 – Logarithmic Functions

Section 6.3 – Logarithmic Functions. Logarithmic Functions. Since the exponential function is 1 – 1, it has an inverse function that is its reflection across the line y = x. This inverse function is called the logarithmic function. This is read, “log base 2 of x.”. Logarithmic Functions.

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Section 6.3 – Logarithmic Functions

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  1. Section 6.3 – Logarithmic Functions

  2. Logarithmic Functions Since the exponential function is 1 – 1, it has an inverse function that is its reflection across the line y = x. This inverse function is called the logarithmic function. This is read, “log base 2 of x.”

  3. Logarithmic Functions Dom: Range: Dom: Range:

  4. Logarithmic Functions Dom: Range: The point (0, 1) is on the graph. y = 0 is a horizontal asymptote base argument/input Dom: Range: The point (1, 0) is on the graph. x = 0 is a vertical asymptote

  5. Logarithmic Functions Function Inverse In an exponential function, you input an exponent and get out a number. In a logarithmic function, you input a number and get out an exponent. Function: Inverse: What exponent must be placed on the base in order for the answer to equal the argument?

  6. Logarithmic Functions What exponent should be placed on the base to give the number in the argument? The domain of a logarithm is Undefined

  7. Logarithmic Functions

  8. Approximating Logarithms Approximate using a calculator or GRAPH. In GRAPH, f(x) = log(x) In GRAPH, f(x) = ln(x) In GRAPH, f(x) = logb(x,3)

  9. Exponential Form Logarithmic Form p. 497: 1 – 57 odd

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