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Properties of Logs

This explanation delves into the derivation of key logarithmic rules, including the Product Rule, Quotient Rule, and Power Rule. By exploring how logb(MN) = logb(M) + logb(N), as well as the implications for logarithmic operations involving division and exponentiation, we clarify the mathematical principles. The derivations reveal the relationships between logarithmic and exponential functions, demonstrating how to interchange bases and apply these rules effectively in problem-solving. Refer to page 443 of your textbook for further insights and examples.

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Properties of Logs

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  1. Properties of Logs

  2. Product Rule LetM= bpand N = bq Then logbM= p andlogbN = q The product MN =bp· bq=bp+q So logbMN=p+q Thus: logbMN = logbM + logbN

  3. Quotient Rule

  4. Power Rule Can you write this derivation? . . . Thus logbMq = q·logbM

  5. Change of Basepage 443 in your book

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