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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.
Chapter 1.4: Logarithm Exercises Calculus I College of the Atlantic. September 26, 2024 1. Answer the following questions without using a calculator. You should be able to explain why the answers are what they are. (a) What is log(1000)? (b) What is log104? (c) What is log(1)? (d) What is log(0)? (e) What is log( 10)? (f) What is log(0:1)?
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.
Logarithms (Introduction) Let aand N be positive real numbers and let N = an:Then nis called the logarithm of Nto the base a. We write this as. n= log. a. N: Examples 1 (a) Since 16 = 24;then 4 = log. 216: (b) Since 81 = 34;then 4 = log. 381: (c) Since 3 = p 9 = 91 2;then 1=2 = log.
Exponential functions are of such importance to mathematics that their inverses, functions that “reverse” their action, are important themselves. These functions, known as logarithms, will be introduced in this lesson. Exercise #1: The function f x . 2x.
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
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.
