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Log Functions

Log Functions. Unit 3. What’s a Log?. The logarithmic function is the inverse of an exponential function. Therefore, a log is an exponent. (just like diving is multiplying by a fraction). Log form Exponential Form. The Base of a Log. b, the base of a log, can be any number…

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Log Functions

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  1. Log Functions Unit 3

  2. What’s a Log? • The logarithmic function is the inverse of an exponential function. • Therefore, a log is an exponent. (just like diving is multiplying by a fraction)

  3. Log form Exponential Form

  4. The Base of a Log b, the base of a log, can be any number… For example, log3 9 = ? log6 216 = ? (the calculator only does log and ln…)

  5. The Base of a Log These bases are frequently used: • Common log – if the base is not written, it is base 10 • Natural log (ln) has a base of e • Remember e is an irrational number with a value of approx. 2.718281828

  6. Characteristics of Log Functions Generally, for b > 0, b ≠ 1, x > 0… • logb 1 = 0 (because…) • logb b = 1 • logb bx = x • b logb x = x

  7. Characteristics of Common Log Functions For base 10 common logs, x > 0 • log 1 = 0 (because…) • log 10 = 1 • log 10x = x • 10 log x = x

  8. Characteristics of Natural Log Functions For base e natural logs, x > 0 • ln 1 = 0 (because…) • ln e = 1 • ln ex = x • eln x = x

  9. Properties of logarithms • Product: logb RS = logb R + logb S • Quotient: logb R = logb R – logb S S • Power: logb Rc = c logb R

  10. Change of Base Formula • Here’s how we can use the calculator to evaluate log34 !! • logb x = log x log b So, log34 = ?

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