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The Logarithm Facts

The Logarithm Facts. Know these…and survive!. The Logarithmic Facts. Fact #1: The logarithmic function is the inverse of the exponential function. Domain: (0,infinity) Range: all real numbers. The Logarithmic Facts. Fact #2: X = b Y  Y = log b X exp. form log form

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The Logarithm Facts

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  1. The Logarithm Facts Know these…and survive!

  2. The Logarithmic Facts Fact #1: The logarithmic function is the inverse of the exponential function. Domain: (0,infinity)Range: all real numbers

  3. The Logarithmic Facts Fact #2: X = bY  Y = logb Xexp. form log form “Your success, or lack of success, with logs is dependent on your ability to change between the two forms.” Pifer

  4. The Logarithmic Facts Fact #3: Logs are exponents!

  5. The Logarithmic Facts Fact #4: Logs of base 10 are called “common logs.” No indicated base means “common log.” The “log” button on your calculator is for common logs.

  6. The Logarithmic Facts Fact #5: Logs of base e are called “natural logs.” Ln means “natural log.” The “ln” button on your calculator is for natural logs.

  7. The Logarithmic Facts Fact #6: Change Of Form Properties • blogbX = X • logbbX = X

  8. The Logarithmic Facts Fact #7: The Continuous Change Formula A = P e r t

  9. The Logarithmic Facts Fact #8: Fundamental Properties: • If a x = a y, then x = y. • If logb x = logb y, then x = y.

  10. The Logarithmic Facts Fact #9: More Fundamental Properties: 1. logb 1 = 0 2. Logbb = 1

  11. The Logarithmic Facts Fact #10: Any positive number can be written as a power of any “legal” base.

  12. The Logarithmic Facts Fact #11: The Log-Product Law log (x y) = log x + log y

  13. The Logarithmic Facts Fact #12: The Log-Quotient Law log (x / y) = log x - log y

  14. The Logarithmic Facts Fact #13: The Log-Power Law log xy = y log x

  15. The Logarithmic Facts Fact #14: The Change of Base Law logbx = log x / log b or logbx = ln x / ln b

  16. The Logarithmic Facts That’s it! Master these facts and you master Logarithms!!

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