Is loge the same as ln

http://pulse.pharmacy.arizona.edu/10th_grade/disease_epidemics/science/medic.htmlAn introduction to the Natural Log(ln)Time:25 minutesPreparation Time: 5 minutesMaterials: Calculators with a log function, graph paperOR Graphing calculator with ln functionORExcel on a computer workstationAbstractTo encourage students’ comprehension of the dose response principle, an introduction to what the “natural log” (ln) is and how it behaves is recommended. This will help students to create and analyze a dose response graph.ObjectivesStudents will be able to: i.Define a log as the inverse of an exponentials.ii.Explain the benefit of a natural log for biologists.iii.Calculate the natural log of a number.iv.Plot a logarithmic graph.Arizona Math Education Standards:Math Strand 2 -Data Analysis, Probability, & Discrete MathematicsConcept 1: Data Analysis (Statistics)PO 1. Formulate questions to collect data in contextual situations.PO 2. Organize collected data into an appropriate graphical representation.PO 3. Display data as lists, tables, matrices, and plotsStrand 5: Structure & LogicConcept 1: Algorithms and Algorithmic ThinkingTeacher BackgroundLogs are the inverse of exponentials. This relationship can be expressed as: bx= y is equivalent tologb(y) = xPronounced "log-base-b of yequals x" "b" is called "the base of the logarithm”The base b for a logarithm is always positive and not equal to 1The value inside the logarithm is called the "argument" of the logA logarithm can be defined with any base, but the most common base is 10 (log on a standard calculator is log base 10)Logarithms with a base e are called the natural logarithm (lnon a calculator)
http://pulse.pharmacy.arizona.edu/10th_grade/disease_epidemics/science/medic.htmlThe natural log is commonly used in biology and engineering because of the "natural" properties of the exponential function which enable it to describe growth or decayeis an irrational number, whose decimal value is approximately 2.71828182845904.Additional Resourceshttp://www.purplemath.com/modules/logs.htmhttp://www.purplemath.com/modules/logs2.htmhttp://www.purplemath.com/modules/logs3.htmhttp://www.purplemath.com/modules/graphlog.htmhttp://www.themathpage.com/alg/logarithms.htmhttp://en.wikipedia.org/wiki/Natural_logarithmActivity1.If you do not have graphing calculators available, distribute graph paper and have students draw a vertical line and horizontal line through the middle of the paper (creating four quadrants). The vertical line will be labeled y, and the horizontal line will be labeled x. 2.Have students solve for y in the exponential t-chart on “The eHandout”. Some calculators may have a function for ex= y (Excel does).3.Now have students convert ex= y to loge(y) = x for the natural log t-chart. Before they begin their calculation, point out that x in both t-charts is exactly the same. Ask them to predict how the graphs may differ.4.Have students graph both t-charts on the same graph. Discuss how they are inverses of one another.5.Relate to the dose-response principle. If dose-response behaves similar to a natural log, what do students expect to happen to an organism’s reaction (response) to a substance as the concentration (dose) increases? How does the curve change for a very strong substance versus a substance of lesser strength?