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explain what is meant by a logarithm. state and use the laws of logarithms. solve simple equations requiring the use of logarithms. Contents. Introduction. Why do we study logarithms ? What is a logarithm ? if x = an then loga x = n. 4. Exercises. 5. The first law of logarithms. loga xy = loga x + loga y. 6. The second law of logarithms.
a > 0, a 6= 1 and b > 0 we have: loga b = c , ac = b. 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.
Chapter 1: Logarithms Used to Calculate Products ..... 1 Chapter 2: The Inverse Log Rules ..... 9 Chapter 3: Logarithms Used to Calculate Quotients ..... 20
Question 2 Simplify each of the following logarithmic expressions, giving the final answer as a single logarithm. a) log 5 log 23 3+ b) log 24 log 82 2− c) log 3 2log 45 5+ d) 3log 8 3log 64 4− e) log 2 3log 3 log 0.256 6 6− +( ) log 102, log 32, log 485, log 4 (6427), log 6 (8) 27
Introduction to Logarithms. -A logarithm is the inverse function for an exponent; therefore, we will review exponential functions first. Review of Exponential Functions. -An exponential function has the general form ( ) = , where 0 < -b is called the base and x is called the exponent. < 1, or > 1.
Name:_______________________. Two areas of application for logarithms are how we measure earthquakes and sound. What are those measurements called? 1. 2. We already know how to solve... 3. How do you say log. We DON’T know how to solve...
2D Introduction to logarithms. In this section we shall look at an operation which reverses the ef ect of exponentiating (raising to a power) and allows us to fi nd an unknown power. If you are asked to solve. x2 3 f x ≥ 0.
