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Question 1 Simplify each of the following logarithmic expressions, giving the final answer as a single logarithm. a) log 7 log 22 2+ b) log 20 log 42 2− c) 3log 2 log 85 5+ d) 2log 8 5log 26 6− e) log 8 log 5 log 0.510 10 10+ − log 142, log 52, log 645, log 26, log 8010
Condense each expression to a single logarithm.
The following examples show how to expand logarithmic expressions using each of the rules above. Use the Power Rule for Logarithms. Since 7a is the product of 7 and a, you can write 7a as 7 • a. Use the Product Rule for Logarithms. 5 3 log = log511 – log53 Use the Quotient Rule for Logarithms.
•solve simple equations requiring the use of logarithms. Contents 1. Introduction 2 2. Why do we study logarithms ? 2 3. What is a logarithm ? if x = an then log a x = n 3 4. Exercises 4 5. The first law of logarithms log a xy = log a x+log a y 4 6. The second law of logarithms log a xm = mlog a x 5 7. The third law of logarithms log a x y ...
Condense each expression to a single logarithm.
Properties of Logarithms -You have probably figured out by now that logarithms are actually exponents! -Due to this, they possess some unique properties that make them even more useful. -In this tutorial we will cover the properties of logarithms and use them to perform expansions and contractions. Property 1: The Power Rule
7.5 Properties of Logarithms Objectives: • Use the properties and laws of logarithms to simplify and evaluate expressions Because logarithms are a special type of exponent, they all share common properties and laws that govern them. These properties and laws allow us to be able to simplify and evaluate logarithmic expressions.
