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Free lessons, worksheets, and video tutorials for students and teachers. Topics in this unit include: what is a logarithm, chain rule, product rule, quotient rule, graphing and transforming logarithmic functions, the natural logarithm, and solving exponential and logarithmic equations.
The following examples show how to expand logarithmic expressions using each of the rules above. Example 1 Expand log 2 49 3 log 2 49 3 = 3 • log 2 49 Use the Power Rule for Logarithms. The answer is 3 • log 2 49 Example 2 Expand log 3 (7a) log 3 (7a) = log 3(7 • a) Since 7a is the product of 7 and a, you can write 7 a as 7 • a. = log 3 ...
Simplify each of the following logarithmic expressions, giving the final answer as a number not involving a logarithm. a) log 24 log 32 2− b) log 96 3log 2 log 43 3 3− − c) 5 5 5 1 2 log 500 log log 10 5 + − d) 2log 54 log 0.25 4log 23 3 3− − e) 8log 2 log 4 3log 96 6 6− −( ) 3 , 1 , 3 , 6 , 6
Worksheet 2:7 Logarithms and Exponentials Section 1 Logarithms The mathematics of logarithms and exponentials occurs naturally in many branches of science. It is very important in solving problems related to growth and decay. The growth and decay may be that of a plant or a population, a crystalline structure or money in the bank. Therefore
Solve the following logarithmic equations. 8. Prove the following statements. 9. Given that log 2 = x, log 3 = y and log 7 = z, express the following expressions in terms of x, y, and z. 10. Solve the following equations. 11. Draw the graph of each of the following logarithmic functions, and analyze each of them completely. 12.
These worksheets provide a variety of problems that cover different aspects of logarithms, such as evaluating logarithmic expressions, solving logarithmic equations, and understanding the properties of logarithms.
solve simple equations requiring the use of logarithms. Why do we study logarithms ? What is a logarithm ? 4. Exercises. 5. The first law of logarithms. 6. The second law of logarithms. 7. The third law of logarithms. 8. 9. 10. 11. 12. 13. 14. 1. Introduction. In this unit we are going to be looking at logarithms.
