Properties of Logarithms - Variable

Remember that log _{b}u (or similarly log_{b}v) is another way to writean exponent.log_{b}u is that exponent you need to raise base "b" to in order t get "u".So the log properties below are just the exponent properties from before. log _{b}Let b, u, and v be positive numbers such that b ≠ 1. bases multiplied together Product Property u v = log _{b}add exponents u + log _{b}v Properties of logarithmslog _{b}Quotient Porperty bases divided u v = log _{b}u subtract exponents - log _{b}v a power to a power log _{b}Power Property u n = n multiply exponents log _{b}u log log_{5}56=log_{5}7•8_{5}56=log_{5}7+log_{5}8log_{5}56≈1.2 + 1.3≈2.5Use the properties of logarithms and the values below to estimate thevalue of the logarithm below. Do not use a calculator to evaluate the log. Product Property Properties of logarithmslog _{7}log_{7}log_{7}Quotient Porperty 12 10 12 10 12 10 =log _{7}12-log_{7}10≈1.3 - 1.2≈0.1log _{3}64=log_{3}8^{2}log_{3}64=2•log_{3}8log _{3}64≈2•1.9≈3.8Power Property Use the properties of logarithms and the values below to estimate thevalue of the logarithm below. Do not use a calculator to evaluate the log. Answer: Properties of logarithmsRound answer to one decimal. If your answer looks like:2.1 enter 2.15 enter 5.0.3 enter 0.3-4.2 enter -4.2Use the properties of logarithms and the values below to estimate thevalue of the logarithm below. Do not use a calculator to evaluate the log. Answer: Properties of logarithmsRound answer to one decimal. If your answer looks like:2.1 enter 2.15 enter 5.0.3 enter 0.3-4.2 enter -4.2Answer: Properties of logarithmsRound answer to one decimal. If your answer looks like:2.1 enter 2.15 enter 5.0.3 enter 0.3-4.2 enter -4.2remember: log _{5}1 = 0Answer: Properties of logarithmsIf your answer looks like:2.1 enter 2.15 enter 5.0.3 enter 0.3-4.2 enter -4.2Answer: Properties of logarithmsIf your answer looks like:2.1 enter 2.15 enter 5.0.3 enter 0.3-4.2 enter -4.2Answer: Properties of logarithmsIf your answer looks like:2.1 enter 2.15 enter 5.0.3 enter 0.3-4.2 enter -4.2Answer: Properties of logarithmsIf your answer looks like:2.1 enter 2.15 enter 5.0.3 enter 0.3-4.2 enter -4.2remember: log _{9}1 = 0Answer: Properties of logarithmsIf your answer looks like:2.1 enter 2.15 enter 5.0.3 enter 0.3-4.2 enter -4.2Answer: Can you make 36 two different ways? Do you get the same answer either way? :) Properties of logarithmsIf your answer looks like:2.1 enter 2.15 enter 5.0.3 enter 0.3-4.2 enter -4.2Answer (yes/no): Answer: Properties of logarithmsIf your answer looks like:2.1 enter 2.15 enter 5.0.3 enter 0.3-4.2 enter -4.2Often there are a combination of properties in one question. Use the properties of logarithms to expand each expression. There should be no powers or radicals in your answer. =log _{9}x^{2}+log_{7}y^{4}=2•log_{9}x+4•log_{7}yProduct Property product & power Properties of logarithms=log _{7}x^{16}-log_{7}y^{4}=16•log_{7}x-4•log_{7}yQuotient Porperty quotient & power =log _{5}z^{2}+log_{5}x^{½}=2•log_{5}z+½•log_{5}x=2•log_{5}z+power and product Power Property log _{5}x2 Use the properties of logarithms and the values below to expand eachexpression. There should be no powers or radicals in your answer. Answer: log _{8}Properties of logarithms+ log _{8}answers should be in orderof increasing logs.i.e log _{6}x+log_{6}y+log_{6}znot log _{6}z+log_{6}y+log_{6}xnot log_{6}y+log_{6}x+log_{6}zUse the properties of logarithms and the values below to expand eachexpression. There should be no powers or radicals in your answer. Answer: log _{7}Properties of logarithms+ log _{7}answers should be in orderof increasing logs.i.e log _{6}x+log_{6}y+log_{6}znot log _{6}z+log_{6}y+log_{6}xnot log_{6}y+log_{6}x+log_{6}zUse the properties of logarithms and the values below to expand eachexpression. There should be no powers or radicals in your answer. Answer: log _{6}+ log _{6}Properties of logarithms+ log _{6}answers should be in orderof increasing logs.i.e log _{6}x+log_{6}y+log_{6}znot log _{6}z+log_{6}y+log_{6}xnot log_{6}y+log_{6}x+log_{6}zAnswer: log _{2}Properties of logarithms- log _{2}Answer: log _{9}Properties of logarithms- log _{9}Answer: log _{9}Properties of logarithms- log _{9}Remember that a radical is a fractional exponent. Rewrite as . . . log(u•v•w) ^{½}½log(u•v•w)Then write as a top:bottom fraction. Answer: log +log Properties of logarithms+log Answer: log _{2}Properties of logarithms+ log _{2}Answer: log _{3}Properties of logarithms+ log _{3}Answer: log _{7}+ Properties of logarithmslog _{7}Often there are a combination of properties in one question. Use the properties of logarithms to condense each expression into asingle logarithm. There should be no + or - in your answer. Product Property =log _{8}(u^{⅓}•v^{⅓}•w^{⅓})=log_{8}(product & power √ 3 u•v•w ) Properties of logarithmsQuotient Porperty quotient & power =log _{7}x^{3}-log_{7}y^{2}^{=log7x3}^{y2}power and product Power Property =log _{5}c^{3}+½log_{5}a=log_{5}c^{3}+log_{5}a^{½}=log_{5}(c^{3}•a^{½})=log_{5}(c^{3}•√ a ) Use the properties of logarithms to condense each expression into asingle logarithm. There should be no + or - in your answer. Answer: ln( • Properties of logarithms• ) Use the properties of logarithms to condense each expression into asingle logarithm. There should be no + or - in your answer. Answer: log _{5}(Properties of logarithms• ) Answer: log _{4}(Properties of logarithms• √ ) Answer: log _{9}(Properties of logarithms) Answer: log _{2}(Properties of logarithms) Answer: log _{4}(Properties of logarithms) Answer: log _{4}(Properties of logarithms• ) Answer: log _{6}(Properties of logarithms) Answer: log( Properties of logarithms) Answer: log _{4}(√ Properties of logarithms• • ) Use the the change of base formula and your calculator to approximatethe value to the nearest thousandths. i.e. answers should look like 3.456 or 0.123 or -6.789 Change of base formula: Your calculator only calculates logarithms with two bases: ten ( base "10") and natural log, ln (base "e"). For other bases, use the conversion below. Properties of logarithmslog _{b}(a) = log(a)log(b) Use the the change of base formula and your calculator to approximatethe value to the nearest thousandths. i.e. answers should look like 3.456 or 0.123 or -6.789 Change of base formula: Example: log _{b}(a) = log(a)log(b) Properties of logarithms= =1.953 log15 log4 = 1.176 0.602 Use the the change of base formula and your calculator to approximatethe value to the nearest thousandths. i.e. answers should look like 3.456 or 0.123 or -6.789 or 6.000 = = = Properties of logarithms= = Use the the change of base formula and your calculator to approximatethe value to the nearest thousandths. i.e. answers should look like 3.456 or 0.123 or -6.789 or 6.000 = = Properties of logarithms= = = |

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