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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
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.
Free 29 question Worksheet(pdf) with answer key on the properties of logarithms (product,quotient and power rules)
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.
Section 2 Properties of Logs Logs have some very useful properties which follow from their de nition and the equivalence of the logarithmic form and exponential form.
Express the equation in exponential form and solve the resulting exponential equation. Simplify the expressions in the equation by using the laws of logarithms.
Detailed step-by-step solutions are provided for each equation to demonstrate how to use logarithmic properties and change of base formulas to transform equations into a form that can be solved algebraically for the variable.
