1 / 7

Understanding Logarithms: The Work of John Napier

This concise guide explores the fundamentals of logarithms as established by John Napier, the creator of logarithms. It covers key concepts such as the definition of logarithms to base b, solving logarithmic equations, and the laws of logarithms for multiplication and division. Additionally, it includes techniques for graphing logarithmic functions and how they share similarities with square root graphs. Whether you're a pre-calculus student or brushing up on mathematics, this resource provides essential insights into the properties and applications of logarithms.

heller
Télécharger la présentation

Understanding Logarithms: The Work of John Napier

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. Logarithms and Their Graphs  John Napier (creator of logarithms) By: Jesus Rocha Period 2 Pre-Calculus

  2. Base b in Logarithm Problems The logarithm to the base b of x,log x, is the power to which you need to raise b in order to get x. log x = y     means     b = x Logarithmic Form Exponential form Rules: 1. Log x is only defined if b and x are both positive, and b ≠1 2. Log x is called the common logarithm of x, and is sometimes written as log 10. 3. Log x is called the natural logarithm of x b b y b 10 e

  3. Solving Logarithms If log 1,000 = 3 (or the logarithm to the base 10 of 1,000 is 3) then its exponential form would be 10 = 1,000 Solving: - Move base 10 to the left of log (10 log 1,000 = 3) - It is easy to figure out that 10 to the power of 3 equals 1,000 so the exponential form would be written as 10 = 1,000 10 3 3

  4. Laws of Logarithms • If the logs are being asked to be multiplied, log x (mn), then you should add the Logs: log m + log n • ex: log (4x8) = log (4) + log (8) = 2+3=5 • If the logs are being asked to be divided, log (m/n), then you should subtract the Logs: log m – log n • ex: log (8/4) = log (8) – log (4) = 3-2=1 • 3. b = 1 b b b 2 2 2 b b b 2 2 2 0

  5. Graphing Logarithms By nature of the logarithms, most log graphs tend to have the same shape, looking similar to a square root graph: Square Root Graph Logarithm Graph

  6. It is simple to graph exponentials. For instance, to graph y = 2x, you would just plug in some values for x, compute the corresponding y-values, and plot the points. A negative number or 0 would make it a little more difficult to solve: - Since 20 = 1, then log (1) = 0, so (1, 0) is on the graph - Since 21 = 2, then log (2) = 1, so (2, 1) is on the graph - Since 22 = 4, then log (4) = 2, so (4, 2) is on the graph - Since 23 = 8, then log(8) = 3, so (8, 3) is on the graph - Since 3, 5, 6, and 7 aren’t powers of 2, they wouldn’t work well with each other 2 2 2 2

  7. The Results

More Related