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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
Logarithm Jeopardy The number e Expand/ Condense LogarithmsSolving More Solving FINAL.
8.5 – Using Properties of Logarithms. Product Property:
You’ve gotten good at solving exponential equations with logs… … but how would you handle something like this?
7.5 NOTES – APPLY PROPERTIES OF LOGS. Condensed formExpanded form Product Property Quotient Property Power Property.
Common Logarithms - Definition Example – Solve Exponential Equations using Logs.
Jeopardy 100 Condense Expand Simplify Solve Exponential Solve Logs 500.
I CAN APPLY PROPERTIES OF LOGARITHMS. Warm-up Can you now solve 10 x – 13 = 287 without graphing? x ≈ 2.48.
Logarithmic Equations Unknown Exponents Unknown Number Solving Logarithmic Equations Natural Logarithms.
Graphs cutting the x and y axis Exponential functions.
5.4 Properties of Logarithms 3/1/2013. Properties of Logarithms Let m and n be positive numbers and b ≠ 1, Product Property Quotient Property Power Property.
LOGARITHMIC AND EXPONENTIAL EQUATIONS LOGARITHMIC AND EXPONENTIAL EQUATIONS SECTION 4.6.
Chapter 5: Exponential and Logarithmic Functions 5.5: Properties and Laws of Logarithms Essential Question: What are the three properties that simplify.
3.3 Properties of Logarithms Change of Base. When solve for x and the base is not 10 or e. We have changed the base from b to 10. WE can change it to.
Review of Logarithms. Review of Inverse Functions Find the inverse function of f(x) = 3x – 4. Find the inverse function of f(x) = (x – 3) Steps.
Table of Contents Logarithm Properties - Quotient Rule The Quotient Rule for logarithms states that... read as “the log of the quotient is the difference.
Unit 5: Modeling with Exponential & Logarithmic Functions Ms. C. Taylor.
Solving Exponential Equations. Example1. Solve. 3 2x+1 = x+1 = 3 4 2x + 1 = 4 2x = 3 x = 3/2.
CONVERTING FROM ONE FORM TO ANOTHER EVALUATING PROPERTIES OF LOGS – EXPANDING AND CONDENSING Day 1:
Solving Logarithmic Equations Chapter 8.6. log with same base on both sides Use this property for logarithms with the same base: log b x = log b y if.
Section 5.3 Properties of Logarithms Advanced Algebra.
Properties of Logarithms Product, Quotient and Power Properties of Logarithms Solving Logarithmic Equations Using Properties of Logarithms Practice.
8.5 Properties of logarithms p Properties of Logarithms Let b, u, and v be positive numbers such that b≠1. Product property: log b uv = log b u.
Aim: What are the properties of logarithms? Do Now: Rewrite the following exponential form into log form 1.b x = A 2.b y = B HW:p.331 # 16,18,20,22,24,26,28,38,40,42,48,52.
NATURAL LOGARITHMS. The Constant: e e is a constant very similar to π. Π = … e = … Because it is a fixed number we can find e 2.
Chapter 3.4 Properties of Log Functions Learning Target: Learning Target: I can find the inverses of exponential functions, common logarithms (base 10),
Natural Logarithms. The number e≈ The function y=e x has an inverse, the natural logarithmic function. If y=e x, then ln y =x.
Holt Algebra Exponential and Logarithmic Equations and Inequalities 7-5 Exponential and Logarithmic Equations and Inequalities Holt Algebra 2 Warm.
ALISON BOWLING LOGARITHMS. LOGARITHMS (BASE 10) 10 0 = 1log 10 1 = = 10log = = 100log = = 1000log =
LOGARITHMIC AND EXPONENTIAL EQUATIONS Intro to logarithms and solving exponential equations.
Properties of Logarithms Tools for solving logarithmic and exponential equations.
Essential Question: What are some of the similarities and differences between natural and common logarithms.
Ch. 3.3 Properties of Logarithms Objectives: 1.) To learn and practice using the change of base theorem 2.) Solving exponentials with the change of base.
Sec 4.3 Laws of Logarithms Objective: To understand the laws of logarithms, including the change of base formula.
8.5 Properties of Logarithms 3/21/2014. Properties of Logarithms Let m and n be positive numbers and b ≠ 1, Product Property Quotient Property Power Property.
Laws of Logarithms 5.6. Laws of Logarithms O If M and N are positive real numbers and b is a positive number such that b 1, then O 1. log b MN = log.
LOGS EQUAL THE The inverse of an exponential function is a logarithmic function. Logarithmic Function x = log a y read: “x equals log base a of y”
These properties are based on rules of exponents since logs = exponents.
Algebra 2 Notes May 4, Graph the following equation: What equation is that log function an inverse of? ◦ Step 1: Use a table to graph the exponential.
8.3-4 – Logarithmic Functions. Logarithm Functions.
3.3 Properties of Logarithms Change of base formula log a x =or.
Property of Logarithms If x > 0, y > 0, a > 0, and a ≠ 1, then x = y if and only if log a x = log a y.
Table of Contents Solving Logarithmic Equations A logarithmic equation is an equation with an expression that contains the log of a variable expression.
Solving Exponential Equations Using Logarithms. Solving Exponential Functions with Logarithms There are three main steps to solving exponential functions.
Properties of Logarithms Section 8.5. WHAT YOU WILL LEARN: 1.How to use the properties of logarithms to simplify and evaluate expressions.
MAC 1105 Section 4.3 Logarithmic Functions. The Inverse of a Exponential Function
Properties of Logarithms Check for Understanding – – Prove basic properties of logarithms using properties of exponents and apply those properties.
Properties of Logarithms: Lesson 53. LESSON OBJECTIVE: 1)Simplify and evaluate expressions using the properties of Logarithms. 2)Solve logarithmic equations.
Do Now: 7.4 Review Evaluate the logarithm. Evaluate the logarithm. Simplify the expression. Simplify the expression. Find the inverse of the function.
SOLVING LOGARITHMIC EQUATIONS Objective: solve equations with a “log” in them using properties of logarithms How are log properties use to solve for unknown.
Exponential Functions Intro. to Logarithms Properties.
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