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Logarithms were originally developed to simplify complex arithmetic calculations. They were designed to transform multiplicative processes into additive ones.
•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 ...
Expand the following logarithms using one or more of the logarithm rules. Sometimes you need to write an expression as a single logarithm. Use the rules to work backwards. log3x2 + log3y . Use the Product Rule for Logarithms. Use the Power Rule for Logarithms. Simplify. Use the Quotient Rule for Logarithms. Simplify. Write as a single logarithm.
We have the following de nition of logarithms: What does it mean? First of all the assumptions (restrictions) are important. The number a, called the base of the logarithm, has to be greater than 0 and cannot be equal to 1. The number b (which we take the logarithm of) has to be greater than 0. 6).
Rewrite each equation in exponential form. Rewrite each equation in logarithmic form. Evaluate each expression. Sketch the graph and identify the domain and range of each. 1. a. Evaluate log27. b. Evaluate . 2. Most tornadoes last less than an hour and travel less than 20 miles.
In this unit you will examine the definition and inverse relationship with the exponential function, practice the laws of logarithms, solve logarithmic equations, and explore a more efficient method for solving equations using the “Change of Base” formula for logarithms.
Rewrite each equation in logarithmic form. Evaluate each expression. Sketch the graph and identify the domain and range of each. 1. a. Evaluate log27. b. Evaluate . 2. Most tornadoes last less than an hour and travel less than 20 miles.
