Properties of Logarithms - Numeric

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 ≈0.1 log _{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 -4.2Answer: 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 _{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 _{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 -4.2remember: 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 -4.2=log _{7}2+log_{7}3+6•log_{7}5Often 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. Product Property product & power Properties of logarithms=log _{7}2^{3}-log_{7}3^{18}=3•log _{7}2-18•log_{7}3Quotient 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 _{4}Properties of logarithms+ log _{4}answers should be in orderof increasing logs.i.e log _{6}7+log_{6}11+log_{6}12not log _{6}12+log_{6}11+log_{6}7not log_{6}11+log_{6}7+log_{6}12Use 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}7+log_{6}11+log_{6}12not log _{6}12+log_{6}11+log_{6}7not log_{6}11+log_{6}7+log_{6}12Use 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}7+log_{6}11+log_{6}12not log _{6}12+log_{6}11+log_{6}7not log_{6}11+log_{6}7+log_{6}12Answer: log _{2}Properties of logarithms- log _{2}Answer: log _{9}Properties of logarithms- log _{9}Answer: log _{3}Properties of logarithms- log _{3}Remember that a radical is a fractional exponent. Rewrite as . . . log _{3}[5•(6•7)^{⅓}]log_{3}[5]+log_{3}(6•7)^{⅓}log_{3}[5]+⅓log_{3}(6•7)Then write as a top:bottom fraction. Answer: log _{3}+log _{3}Properties of logarithms+log _{3}_{6}7+log_{6}11+log_{6}12not log _{6}12+log_{6}11+log_{6}7not log_{6}11+log_{6}7+log_{6}12Answer: log _{6}Properties of logarithms- log _{6}Answer: log _{6}Properties of logarithms+ log _{6}_{6}7+log_{6}11+log_{6}12not log _{6}12+log_{6}11+log_{6}7not log_{6}11+log_{6}7+log_{6}12Answer: log _{7}Properties of logarithms+ log _{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 _{6}(3•2^{⅓}•7^{⅓})=log_{6}(3•=log_{6}(3•product & power √ √ 3 3 2•7 14 ) ) Properties of logarithmsQuotient Porperty quotient & power =log _{7}2^{4}-log_{7}3^{24}^{=log724}^{324}power and product Power Property =log7 ^{3}+⅓log8=log7^{3}+log8^{⅓}=log(7^{3}•8^{⅓})=log(7^{3}•√ 3 8 ) Use the properties of logarithms to condense each expression into asingle logarithm. There should be no + or - in your answer. Answer: log _{3}(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 _{8}(Properties of logarithms• √ ) Answer: log _{4}(Properties of logarithms• √ ) Answer: log _{6}(Properties of logarithms) Answer: log _{8}(Properties of logarithms) Answer: log _{7}(Properties of logarithms) Answer: log _{8}(Properties of logarithms• √ ) Answer: log _{9}(Properties of logarithms• ) Answer: log _{3}(Properties of logarithms) Answer: log _{2}(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= log15 = 1.176 log4 0.602 =1.953 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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