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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.
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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
©Y 32 P0n1 Q1j jKXumtIa o 2S 5o hfYtIw haYr3ex eL oLLCR.z d IA yl7lQ Sr biIgLhbtXsG 9r YeRsaehrPvJeid q.7 H 6M da GdGeQ 3wui WtMhQ hIln AfBionLiYtVep VAUlCgGeBb0rhaz K2K.F Worksheet by Kuta Software LLC Condense each expression to a single logarithm. 13) log 3 − log 8 14) log 6 3 15) 4log 3 − 4log 8 16) log 2 + log 11 + log 7
Free 29 question Worksheet (pdf) with answer key on the properties of logarithms (product,quotient and power rules)
Properties of Logarithms. Condense each expression to a single logarithm. 1) 4log 10 - 6log 3. 9 9. 3) 4log 7 + 24log. 9 10. 9. 5) log x + log y + 4log z. 5 5 5.
A logarithm has various important properties that prove multiplication and division of logarithms can also be written in the form of logarithm of addition and subtraction. We will learn more about it in the benefits of properties of logarithm worksheets.
