Αποτελέσματα Αναζήτησης
•explain what is meant by a logarithm •state and use the laws of 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 ...
A logarithm is just an index. We use log as an abbreviation for the word logarithm. To find the value of a logarithm we need to solve an exponential equation. Example (a) The solution of 2x = 8 is x = 3. We can write this in logarithm notation as log 2 8 = 3 ‘log of 8 to base 2 is 3’ (b) x = 5 is the solution of 2x = 32.
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. We have the following de nition of logarithms: What does it mean?
What are some of the characteristics of the graph of a logarithmic function? other than 1, has an inverse function that you can denote by g(x) = logb x. This inverse function is called a logarithmic function with base b. Work with a partner. Find the value of x in each exponential equation. Explain your reasoning.
If a > 1 or 0 < a < 1, then the exponential function f : R ! (0, defined 1) as f (x) = ax is one-to-one and onto. That means it has an inverse function. If either a > 1 or 0 < a < 1, then the inverse of the function ax is. loga : (0, 1) ! and it’s called a logarithm of base a. Problem. Find x if 2x = 15. Solution.
Chapter 1: Logarithms Used to Calculate Products ..... 1 Chapter 2: The Inverse Log Rules ..... 9 Chapter 3: Logarithms Used to Calculate Quotients ..... 20
terms of logarithms: KEY POINT 2.21 Th e logarithm of 1 is always 0, irrespective of the base. g a 10 We can use the laws of logarithms to manipulate expressions and solve equations involving logarithms, as the next two examples illustrate. Worked example 2.8 If xalog 10 and yb, express log 10 100a2 b in terms of x, y and integers. Use laws of ...
