1 / 9

Properties of Logarithms

Properties of Logarithms. The Product Rule. Let b , M , and N be positive real numbers with b  1. log b (MN) = log b M + log b N The logarithm of a product is the sum of the logarithms. For example, we can use the product rule to expand ln (4 x ): ln (4 x ) = ln 4 + ln x . æ .

JasminFlorian
Download Presentation

Properties of Logarithms

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Properties of Logarithms

  2. The Product Rule Let b, M, and N be positive real numbers with b 1. logb (MN) = logbM + logbN The logarithm of a product is the sum of the logarithms. For example, we can use the product rule to expand ln (4x): ln (4x) = ln 4 + ln x.

  3. æ ö M log ç ÷ = log M - log N è ø b N b b The Quotient Rule Let b, M and N be positive real numbers with b  1. The logarithm of a quotient is the difference of the logarithms.

  4. The Power Rule Let b, M, and N be positive real numbers with b = 1, and let p be any real number. log bM p = p log bM The logarithm of a number with an exponent is the product of the exponent and the logarithm of that number.

  5. Solution a. log4 2 + log4 32 = log4 (2 • 32) Use the product rule. = log4 64 Although we have a single logarithm, we can simplify since 43 = 64. = 3 Text Example Write as a single logarithm: a. log4 2 + log4 32

  6. Problems Write the following as single logarithms:

  7. The Change-of-Base Property For any logarithmic bases a and b, and any positive number M, The logarithm of M with base b is equal to the logarithm of M with any new base divided by the logarithm of b with that new base.

  8. Solution Because Solution Because This means that This means that Example: Changing Base to Common Logs Use common logarithms to evaluate log5 140. Example: Changing Base to Natural Logs Use natural logarithms to evaluate log5 140.

  9. Use logarithms to evaluate log37. Solution: Example or so

More Related