5ln x y 2 ln y 8ln x ln x y ln y 2

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Unformatted text preview: ath.lamar.edu/terms.aspx College Algebra Note that all of the properties given to this point are valid for both the common and natural logarithms. We just didn’t write them out explicitly using the notation for these two logarithms, the properties do hold for them nonetheless Now, let’s see some examples of how to use these properties. Example 4 Simplify each of the following logarithms. (a) log 4 ( x3 y 5 ) [Solution] æ x9 y5 ö 3÷ èz ø (b) log ç (c) ln xy [Solution] [Solution] æ ( x + y )2 ö (d) log 3 ç 2 ÷ ç x + y2 ÷ è ø [Solution] Solution The instructions here may be a little misleading. When we say simplify we really mean to say that we want to use as many of the logarithm properties as we can. ( (a) log 4 x3 y 5 ) Note that we can’t use Property 7 to bring the 3 and the 5 down into the front of the logarithm at this point. In order to use Property 7 the whole term in the logarithm needs to be raised to the power. In this case the two exponents are only on individual terms in the logarit...
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This note was uploaded on 06/06/2012 for the course ICT 4 taught by Professor Mrvinh during the Spring '12 term at Hanoi University of Technology.

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