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4.4 – Evaluate Logarithms and Graph Logarithmic Functions

4.4 – Evaluate Logarithms and Graph Logarithmic Functions. GPS: MM3A2c, MM3A2e, MM3A2f. GPS. MM3A2c – Define logarithmic functions as inverses of exponential functions. MM3A2f – Graph functions as transformations of f(x) = a x , f(x) = log a x, f(x) = ex, f(x) = ln x.

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4.4 – Evaluate Logarithms and Graph Logarithmic Functions

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  1. 4.4 – Evaluate Logarithms and Graph Logarithmic Functions GPS: MM3A2c, MM3A2e, MM3A2f

  2. GPS • MM3A2c – Define logarithmic functions as inverses of exponential functions. • MM3A2f – Graph functions as transformations of f(x) = ax, f(x) = logax, f(x) = ex, f(x) = ln x. • MM3A2e – Investigate and explain characteristics of exponential and logarithmic functions including domain and range, asymptotes, zeros, intercepts, intervals of increase and decrease, and rate of change.

  3. Vocabulary • Let b and y be positive numbers with b≠ 1. The logarithm of y with base b is denoted by and is defined as follows: = x if and only if • A common logarithm is a logarithm with base 10, denoted by log. • A natural logarithm is a logarithm with base e, denoted by ln. • A logarithmic function is a function of the form . • By definition of a logarithm, it follows that the logarithmic function is the inverse of the exponential function .

  4. Example 1: Rewrite logarithmic equations (Page 145)

  5. Example 2: Evaluate logarithms • Evaluate the logarithm.

  6. Guided Practice • Try page 145, 1-8

  7. What are these?

  8. What are Inverses? • Before we answer that, what is a function? • Think maps • How would we solve the following functions? Range Domain 2 3

  9. Steps to finding the inverse of a function • Switch the x and y • Solve for y • How do we get rid of different things like logs or natural logs? • Denote by using thefollowing: • Logs are “undone” by exponents – and vice versa • Natural logs (ln) are undone by e – or vice versa

  10. Example

  11. Find inverse function (Page 146) • Find the inverse of the function. • From the definition of logarithm, the inverse of is

  12. Translate a logarithmic graph • Graph State the domain and range. Same rules apply

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