Αποτελέσματα Αναζήτησης
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
Solutions for practice problems in 3.3 Properties of logarithms 1. Expand these to a sum/difference of logs. log ab2 c ln a 2b 3 2. Put these in a single logarithmic expression. lna 3lnb 1 2 lnc 2loga 5logb
The following examples show how to expand logarithmic expressions using each of the rules above. Use the Power Rule for Logarithms. Since 7a is the product of 7 and a, you can write 7a as 7 • a. Use the Product Rule for Logarithms. 5 3 log = log511 – log53 Use the Quotient Rule for Logarithms.
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.
Practice for 3.3 Properties of logarithms The following problems will help you practice the material you learned today. Once you are finished check your solutions. Once done, you can work on your WeBWorK homework. 1. Expand these to a sum/difference of logs. log. ab. 2. c. ln. a. 2. b 3. 2. Put these in a single logarithmic expression. ln. a ...
Logs have some very useful properties which follow from their de nition and the equivalence of the logarithmic form and exponential form. Some useful properties are as follows:
Express the equation in exponential form and solve the resulting exponential equation. Simplify the expressions in the equation by using the laws of logarithms.
