8-2 Properties of Exponential Functions

8-2 Properties of Exponential Functions

8-5 Exponential and Logarithmic Equations Solving logarithmic & exponential equations Objectives Solving Exponential Equations Solving Logarithmic Equations Vocabulary An equation of the form bcx = a is and exponential equation. If m = n, then log m = log n Solving an Exponential Equation Solve log 52x = 16.

52x = 16 52x = log 16 Take the common logarithm of each side. 2x log 5 = log 16 Use the power property of logarithms. log 16 x= 2 log 5 Divide each side by 2 log 5. 0.8614 Check: 52x

52(0.8614) 16 16 Use a calculator. Solving an Exponential Equation by Graphing Solve 43x = 1100 by graphing. Graph the equations y = 43x and y = 1100. Find the point of intersection. The solution is x 1.684

Continued (continued) 1.387 log 3 log x Multiply each side by log 3. 1.387 0.4771 log x Use a calculator. 0.6617 log x

Simplify. 100.6617 Write in exponential form. 4.589 Use a calculator. x The expression log6 12 is approximately equal to 1.3869, or log3 4.589. Solving an Exponential Equation by Tables

Solve 52x = 120 using tables. Enter y1 = 52x 120. Use tabular zoom-in to find the sign change, as shown at the right. The solution is x 1.487. Real-World Example The population of trout in a certain stretch of the Platte River is shown for five consecutive years in the table, where 0 represents the year 1997. If the decay rate remains constant, in the beginning of which year might at most 100 trout remain in this stretch of river? Time t Pop. P(t) 0

1 2 3 4 5000 4000 3201 2561 2049

Step 1: Enter the data into your calculator. Step 2: Use the Exp Reg feature to find the exponential function that fits the data. Continued (continued) Step 3: Graph the function and the line y = 100. Step 4: Find the point of intersection. The solution is x 18, so there may be only 100 trout remaining in the beginning of the year 2015. Vocabulary For any positive numbers, M, b, c, with b 1 and c 1,

logcM logbM = logcb Using the Change of Base Formula Use the Change of Base Formula to evaluate log6 12. Then convert log6 12 to a logarithm in base 3. log6 12 = log 12 log 6 1.0792 0.7782 log6 12 = log3 x Use the Change of Base Formula. 1.387

Use a calculator. Write an equation. 1.387 log3x Substitute log6 12 = 1.3868 1.387 log x log 3 Use the Change of Base Formula. Solving a Logarithmic Equation

Solve log (2x 2) = 4. log (2x 2) = 4 2x 2 = 104 Write in exponential form. 2x 2 = 10000 x = 5001 Solve for x. Check: log (2x 2) 4 log (2 5001 2)

4 log 10,000 4 log 104 = 4 Using Logarithmic Properties to Solve an Equation Solve 3 log x log 2 = 5. 3 log x log 2 = 5 Log ( x ) = 5 2 x3 = 105 2 3

Write as a single logarithm. Write in exponential form. x3 = 2(100,000) 3 x = 10 The solution is 10 3 Multiply each side by 2. 200, or about 58.48. 200, or about 58.48.

Homework 8-5 Pg 464 # 1, 2, 13, 14, 23, 25, 26, 33, 34, 42, 43

Recently Viewed Presentations

  • CSCI 203 Introduction to Computer Science I

    CSCI 203 Introduction to Computer Science I

    CSCI 203 Introduction to Computer Science I Last modified by: Xiannong Meng ...
  • Everyday Leadership - STF

    Everyday Leadership - STF

    A world-class skills infrastructure for work-based learning, which contributes to economic growth by increasing the productivity of individuals through skills development. ... First pathfinder cohorts complete / graduate. New FA frameworks developed.
  • Progressive Energy Dynamics (The Key to Low Standoff

    Progressive Energy Dynamics (The Key to Low Standoff

    Fluid Flow Theory - Cleaning Small Gaps Depends on 2 things. . . 1. Physical properties of the cleaning agent (surface tension, density and viscosity) 2. Higher energy fluid delivery (flow rate and impact velocity) Energy Delivered is dependent on...
  • Benefit Options 2019

    Benefit Options 2019

    Premier Dentist has higher out-of-pocket costs for member. Cigna. Prepaid means dentists accept set fees. Has a more narrow network. Make sure your dentist is on the network you are choosing. Refer to the guide for the list of states...
  • Πληροφοριακά Συστήματα

    Πληροφοριακά Συστήματα

    Πανεπιστήμιο Αιγαίου Τμήμα Μηχανικών Σχεδίασης Προϊόντων & Συστημάτων Ε΄ εξάμηνο
  • Acute Stroke Diagnosis: science and art

    Acute Stroke Diagnosis: science and art

    Yes, if: The time of onset of stroke symptoms is known precisely You have an experienced stroke physician/stroke neurologist able to see the patient urgently in A&E or at CT scan room Urgent non-contrast CT scan is interpreted by someone...
  • Ozone Depletion I - Colby College

    Ozone Depletion I - Colby College

    Gradual liberalization, mitigated by government policies? Strengthen international institutions? Tackle poverty? Globalization and Its Discontents IR Theories on the EU Liberalism Institutions Domestic politics and intergovernmental bargains Functionalism - functional spillover Constructivism Norms of democratic community Realism?
  • Rhetoric and Composition - Web.nmsu.edu

    Rhetoric and Composition - Web.nmsu.edu

    Rhetoric and Composition Skills and methods used in writing university-level essays. Rhetoric So What is Rhetoric? Rhetoric Aristotle's definition Let rhetoric be an ability, in each case, to see the means available of persuasion. This is the function of no...