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Unformatted text preview: 6-5: Properties of LogarithmsProperties: (1) alog=1and alog a=1; (2) alogMaM=and ralog ar=;(3) (29aaalogMNlog Mlog N=+; (4) aaaMloglog Mlog NN=-; (5) raalog Mr log M=; (6) aaloglog NN= -1. If M, N, and a are positive real numbers and a 0 and b0, then (7) if M = N, aalog Mlog N=, and (8) if aalog Mlog N ,=M = N. Change of base formulas: (9) bablog Mlog Mlog a=and (10) aln Mlog Mln a=.Use the properties of logarithms to find the exact value of each expression. Do not use a calculator:1.ln e22.loglog+66943.loglog+55675Write as the sum or difference of logarithms:4.( 29ln xx+4215.bx ylogz52366.(29 - - xlnx223241Express as a single logarithm:7.loglogxx+222118.(29bbblog x log x log y+ -2 39.logxlogxlog+ -233332192510.( 29744435log 2 2log 5 3log 3x x+ -Evaluate; round your answer to nearest hundredth.11.log1/215 =12.log51813....
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- Fall '08