4_4 - N ) = log a M-log a N where 0 < a 6 =...

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Section 4.4: Properties of Logarithms Instructor: Ms. Hoa Nguyen (nguyen@scs.fsu.edu) 1 Basic properties The logarithmic function y = log a x with 0 < a 6 = 1 and the exponential function y = a x with 0 < a 6 = 1 are the inverse of each other. In other words, p = log R L ⇐⇒ L = R p . Due to the inverse, we have the following basic properties: log a 1 = 0 because a 0 = 1. log a a = 1 because a 1 = a . a log a x = x log a a x = x Example 1 : The Log of a Product equals the Sum of the Logs: log a ( MN ) = log a M + log a N where 0 < a 6 = 1, M, N > 0. Consequently, log a M r = rlog a M . Example 2 : 1
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Example 3 : Example 4 : The Log of a Quotient equals the Difference of the Logs: log a ( M
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Unformatted text preview: N ) = log a M-log a N where 0 &amp;lt; a 6 = 1, M, N &amp;gt; 0. Consequently, log a ( 1 M ) = log a 1-log a M =-log a M . Example 5 : Example 6 : 2 Example 7 : log a M = log a N M = N (0 &amp;lt; a 6 = 1, M, N &amp;gt; 0). 2 Change-of-Base Formula If 0 &amp;lt; a 6 = 1, 0 &amp;lt; b 6 = 1 and M &amp;gt; 0, then log a M = log b M log b a (change from base a to base b ). Consequently, use the above formula to change to base e ( ln ) or base 10 ( log ): log a M = lnM lna . log a M = logM loga . Example 8 : Example 9 : 3...
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4_4 - N ) = log a M-log a N where 0 &amp;amp;amp;lt; a 6 =...

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