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Logarithms By: Lulu Huang, Alison Li,Gladi Pang Period 4
8-4 Properties of Logarithms Product Property: log b XY = log b X + log b Y Quotient Property : log b X = log b X - log b Y Y Power property: log b X y = ylogbX
8-4 Identifying Properties Example 1: log5 + log6 = log 30 product property Example 2: log log log 5 4 = log 5 25 product and quotient property
8-4 Simplifying Logarithms Example 1: log log 4 32 = log 4 (4 x 32) = log Example 2: log 7 X + log 7 Y - log 7 Z = log 7 (X x Y) Z = log 7 XY Z
8-4 Expanding Logarithms Example 1: log 5 XY = log 5 X + log 5 Y Example 2: log3m4n -2 = log3 + logm4 +logn -2 = log3 + 4logm + -2logn
8-5 Solving Exponential Equation Example 1: 7 2X = 25 log7 2X = log25 2Xlog7 = log25 log7 log 7 2X = X = Example 2: 20 2X+1 = 260 log20 2X+1 = log260 2X+1log20 = log260 log 20 log 20 2X+1 = X = X =
8-5 Using Change Of Base Formula Change Of Base Formula: log a N = log N log a Example 1: log 3 33 = log33 log 3 Example 2: log = log135 log5
8-5 Solving Exponential Equations by Changing Base Example 1: 2X = 5 log 2 2 X = log 2 5 Xlog 2 2 = log 2 5 Xlog2 = log5 log2 log2 X = Example 2: 7 3X+4 = 79 log 7 7 3X+4 = log X + 4 log7 = log79 log7 log7 3X + 4 = X = x =
8-5 Solving a Logarithmic Equations 2 X2X2 = 100 2
8-5 Using Logarithmic Properties to Solve Equation
8-6 Simplifying Natural Logarithms Example 1: 3 ln 5 ln 5 3 = ln125 = 4.83 Example 2: ln a - 2 ln b + 2 ln c = ln a - ln b 2 + ln c 2 = ln a x c 2 b 2 = ln ac 2 b 2
8-6 Solving Natural Logarithmic Equations
8-6 Solving Exponential Equations
Logarithmic Equations Solving Logarithmic Equations.
Solving Exponential and Logarithmic Equations Section 3.4 JMerrill, 2005 Revised, 2008.
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Unit 6. For x 0 and 0 a 1, y = log a x if and only if x = a y. The function given by f (x) = log a x is called the logarithmic function with base.
5.5 Properties and Laws of Logarithms Do Now: Solve for x. x = 3 x = 12 x = 6 x = 1/3.
Properties of Logarithmic Functions Objective: Simplify and evaluate expressions involving logarithms.
Warm-Up Solve each equation for x. Round your answers to the nearest hundredth. 4 minutes 1) 10 x = ) 10 x = Find the value of x in each.
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Mrs. McConaughyHonors Algebra 21 Properties of Logarithms During this lesson, you will: Expand the logarithm of a product, quotient, or power Simplify.
Warm Up 1)Sketch the graph of y = ln x a)What is the domain and range? b)Determine the concavity of the graph. c)Determine the intervals where the graph.
A logarithm with a base of e is called a natural logarithm and is abbreviated as “ln” (rather than as log e ). Natural logarithms have the same properties.
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3.3 Logarithmic Functions and Their Graphs We learned that, if a function passes the horizontal line test, then the inverse of the function is also a function.
Copyright © Cengage Learning. All rights reserved. 3 Exponential and Logarithmic Functions.
Differentiation of the Exponential Function (e x ) and Natural Logarithms (lnx) Exponential function e x.
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SOLVING EQUATIONS AND EXPANDING BRACKETS AIM: USE FLOWCHARTS TO SOLVE EQUATIONS A + 5 = 12 A A A = 7 3C = 12 C 3 12 C = 4.
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Section 5.4 – Properties of Logarithms. Simplify:
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8.3 – Logarithmic Functions and Inverses. What is a logarithm? A logarithm is the power to which a number must be raised in order to get some other number.
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