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Big Ideas Math Algebra 2 A Bridge to Success
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Big Ideas Math Algebra 2 A Bridge to Success View details
3. Logarithms and Logarithmic Functions
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Exercise 4 Page 309

Logarithmic functions f(x) = log_b x are the inverse of exponential functions g(x) = b^x.

See solution.

Practice makes perfect
Since logarithmic functions f(x) = log_b x are the inverse of exponential functions g(x) = b^x, we can deduce some of their properties from those of exponential functions. For example, if g(x) = b^x passes through (0,1) then f(x) = log_b x passes through (1,0). Let's summarize some of the main characteristics for logarithmic functions.

In any logarithmic function of the form f(x) log_b x, we can identify the characteristics shown below.

  • A logarithmic function is continuous, as its graph presents no gap.
  • The range is all real numbers, (- ∞, +∞).
  • The domain is all real numbers greater than 0, (0, +∞).
  • The graph approaches to either when +∞, or - ∞ when x approaches 0.
  • The graph has no y-intercepts.
  • The graph always includes the point (1,0).
  • The graph always includes the point (b,1).
Subchapter links expand_more
arrow_right Communicate Your Answer p.309
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arrow_right Monitoring Progress p.311-313
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arrow_right Exercises p.314-316
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