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Logarithmic Functions

Logarithmic Functions. What you need to know. Students are to develop an understanding of the relationship between exponential and logarithmic expressions The graph of exp(x) and log(x) are inverses of one another Graphically they are reflected along the line y=x

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Logarithmic Functions

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  1. Logarithmic Functions

  2. What you need to know Students are to develop an understanding of the relationship between exponential and logarithmic expressions The graph of exp(x) and log(x) are inverses of one another Graphically they are reflected along the line y=x How does knowing the inverse give you information about the function?

  3. The graphs of log(x) The graph of log(x) is represented in this graph Through investigation with and without technology students learn key features such as vertical and horizontal asymptotes, domain and range, intercepts, increasing /decreasing behaviour

  4. Properties of exp(x) Properties of log(x) Domain: All real numbers Range: All positive Real numbers Intercepts: dependent on the value of a, f(x) = aexp(x) Domain: Range: Intercepts:

  5. Properties of Logarithms • loga(xy)= logax + logay • loga (x/y )= logax –logay • loga(xr)= r logax • logaa =1          loga1 =0 • loga (1/x) = -logax • log216 = log28 + log22 • log2 (5/3) = log25 - log23 • log2(65) = 5 log26 • log22=1 log31 =0 • log2 (1/3) = -log23

  6. So What is the Differences in College and University Content? • ....?

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