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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
8. Prove the following statements. (1) logp b x = 2log x (2) log p1 b p x = log x (3) log 4 x2 = log p x 9. Given that log2 = x, log3 = y and log7 = z, express the following expressions
The following examples show how to expand logarithmic expressions using each of the rules above. Example 1. Expand log2493 . log2493 = 3 • log249 . The answer is 3 • log249. Use the Power Rule for Logarithms. Example 2. Expand log3(7a) log3(7a) = log3(7 • a) = log37 + log3a. The answer is log37 + log3a.
Free 29 question Worksheet (pdf) with answer key on the properties of logarithms (product,quotient and power rules)
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. Represent the sums or differences of logs as single logarithms. Square all logarithmic expressions and solve the resulting quadratic equation. ____ 13.
Solutions for practice problems in 3.3 Properties of logarithms . 1. Expand these to a sum/difference of logs. ab2. log. Put these in a single logarithmic expression. lnc. 3. If log 2 = .301 and log 3 =.477, determine the value of these by turning them into expressions involving only log 2 and log 3.
