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Warm Up: Simplify the Expression. Then State briefly how to simplify the exponents. 1. 2. 3.
4-5 Properties of Logarithms
Ex 1: Condense the Expression a. b. Remember that Multiplication and Addition go hand-in-hand. We must have the same base to condense!!! ln is in base e. Division and Subtraction go hand-in-hand.
Ex 3: Condense the Expression Here, the distributive law can be used.
Let’s Put it all together… Ex 4&5: Condense the expression.
We can Also go Backwards! We can also “un-distribute” the exponent Ex6: Expand the expression.
We can Also go Backwards!! Ex 6&7: Expand the expression.
Ex 7: Use log 3 ≈.477 and log 2 ≈.301 to approximate the value of the expression
The Change of Base Formula Let u, b, and c be positive numbers with b≠1 and c≠1. Then: More specifically:
Ex 8: Use the change of base formula to evaluate the expression
Ex 1: Use properties of logarithms to evaluate the expression = ? a. b.
Properties of Logarithms Section 8.5. WHAT YOU WILL LEARN: 1.How to use the properties of logarithms to simplify and evaluate expressions.
Laws (Properties) of Logarithms
Expanding and Condensing Logarithms Product Property.
EXPANDING AND CONDENSING LOGARITHMS PROPERTIES OF LOGARITHMS Product Property: Quotient Property: Power Property: PROPERTIES OF LOGARITHMS.
3.3 Properties of Logarithms Change of base formula log a x =or.
8.5 Properties of logarithms
Section 5.3 Properties of Logarithms Advanced Algebra.
Section 5.6 Laws of Logarithms (Day 1)
Properties of Logarithms. The Product Rule Let b, M, and N be positive real numbers with b 1. log b (MN) = log b M + log b N The logarithm of a product.
10.5 Properties of Logarithms. Remember…
8d - Properties of Logarithms. Product Property Here is the product property: Using this form, expand the following: In order to simplify, use the product.
Logarithms of Products
Logarithm Jeopardy The number e Expand/ Condense LogarithmsSolving More Solving FINAL.
Exponential Function An exponential function with base b and exponent x is defined by Ex. Domain: All reals Range: y > 0 (0,1) x y.
Properties of Logarithms
WARM - UP Evaluate: log 3 81 Solve for x: log5 (2x+3) = log5 (4x -3)
4.5 Apply Properties of Logarithms p. 259 What are the three properties of logs? How do you expand a log? Why? How do you condense a log?
7.5 NOTES – APPLY PROPERTIES OF LOGS. Condensed formExpanded form Product Property Quotient Property Power Property.
Unit 11: Logarithms, day 3 3 properties to Expand and Condense Logarithmic Expressions.
Warm-Up 1) Use log 3 5 = and log 3 6 = to approximate log ) Condense 7 log log 4 x + 3 log 4 y.
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