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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
•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 ...
4 Free worksheets with answer keys on logarithms. Each one has model problems worked out step by step, practice problems and challenge proglems
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. = logbX – logbY. logb(XY) = logbX + logbY Power Rule for Logarithms. Quotient Rule for Logarithms. Product Rule for Logarithms. 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.
Rules of Logarithms. loga x = y () ay = x. aloga M = M. loga a = 1. log 1 = 0. loga Mr = r loga M. log a(M N) = log M + log. N. log a(M ) = log M.