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Remember that logbu (or similarly logbv) is another way to writean exponent.logbu 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. logb Let b, u, and v be positive numbers such that b ≠ 1. bases multiplied together Product Property u v = logb add exponents u + logb v Properties of logarithms logb Quotient Porperty bases divided u v = logb u subtract exponents - logb v a power to a power logb Power Property u n = n multiply exponents logb u log556=log57•8 log556=log57+log58log556≈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 logarithms log7log7log7 Quotient Porperty 12 10 12 10 12 10 =log712-log710 ≈1.3 - 1.2 ≈0.1 log364=log382 log364=2•log38 log364≈2•1.9≈3.8 Power 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 logarithms Round answer to one decimal. If your answer looks like: 2.1 enter 2.15 enter 5.0.3 enter 0.3-4.2 enter -4.2 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 logarithms Round answer to one decimal. If your answer looks like: 2.1 enter 2.15 enter 5.0.3 enter 0.3-4.2 enter -4.2 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 logarithms Round answer to one decimal. If your answer looks like: 2.1 enter 2.15 enter 5.0.3 enter 0.3-4.2 enter -4.2 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 logarithms Round answer to one decimal. If your answer looks like: 2.1 enter 2.15 enter 5.0.3 enter 0.3-4.2 enter -4.2 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. remember: log51 = 0 Answer: Properties of logarithms Round answer to one decimal. If your answer looks like: 2.1 enter 2.15 enter 5.0.3 enter 0.3-4.2 enter -4.2 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 logarithms Round answer to one decimal. If your answer looks like: 2.1 enter 2.15 enter 5.0.3 enter 0.3-4.2 enter -4.2 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 logarithms Round answer to one decimal. If your answer looks like: 2.1 enter 2.15 enter 5.0.3 enter 0.3-4.2 enter -4.2 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 logarithms Round answer to one decimal. If your answer looks like: 2.1 enter 2.15 enter 5.0.3 enter 0.3-4.2 enter -4.2 remember: log51 = 0 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 logarithms Round answer to one decimal. If your answer looks like: 2.1 enter 2.15 enter 5.0.3 enter 0.3-4.2 enter -4.2 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. remember: log51 = 0 Answer: Properties of logarithms Round answer to one decimal. If your answer looks like: 2.1 enter 2.15 enter 5.0.3 enter 0.3-4.2 enter -4.2 =log72+log73+6•log75 Often 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 =log723-log7318 =3•log72-18•log73 Quotient Porperty quotient & power =log5z2+log5x½=2•log5z+½•log5x=2•log5z+ power and product Power Property log5x 2 Use the properties of logarithms and the values below to expand eachexpression. There should be no powers or radicals in your answer. Answer: log4 Properties of logarithms + log4 answers should be in orderof increasing logs.i.e log67+log611+log612 not log612+log611+log67not log611+log67+log612 Use the properties of logarithms and the values below to expand eachexpression. There should be no powers or radicals in your answer. Answer: log8 Properties of logarithms + log8 answers should be in orderof increasing logs.i.e log67+log611+log612 not log612+log611+log67not log611+log67+log612 Use the properties of logarithms and the values below to expand eachexpression. There should be no powers or radicals in your answer. Answer: log6 +log6 Properties of logarithms +log6 answers should be in orderof increasing logs.i.e log67+log611+log612 not log612+log611+log67not log611+log67+log612 Use the properties of logarithms and the values below to expand eachexpression. There should be no powers or radicals in your answer. Answer: log2 Properties of logarithms - log2 Use the properties of logarithms and the values below to expand eachexpression. There should be no powers or radicals in your answer. Answer: log9 Properties of logarithms - log9 Use the properties of logarithms and the values below to expand eachexpression. There should be no powers or radicals in your answer. Answer: log3 Properties of logarithms - log3 Use the properties of logarithms and the values below to expand eachexpression. There should be no powers or radicals in your answer. Remember that a radical is a fractional exponent. Rewrite as . . . log3[5•(6•7)⅓]log3[5]+log3(6•7)⅓log3[5]+⅓log3(6•7) Then write as a top:bottom fraction. Answer: log3 +log3 Properties of logarithms +log3 answers should be in orderof increasing logs.i.e log67+log611+log612 not log612+log611+log67not log611+log67+log612 Use the properties of logarithms and the values below to expand eachexpression. There should be no powers or radicals in your answer. Answer: log6 Properties of logarithms - log6 Use the properties of logarithms and the values below to expand eachexpression. There should be no powers or radicals in your answer. Answer: log6 Properties of logarithms + log6 answers should be in orderof increasing logs.i.e log67+log611+log612 not log612+log611+log67not log611+log67+log612 Use the properties of logarithms and the values below to expand eachexpression. There should be no powers or radicals in your answer. Answer: log7 Properties of logarithms + log7 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 =log6(3•2⅓•7⅓)=log6(3•=log6(3• product & power √ √ 3 3 2•7 14 ) ) Properties of logarithms Quotient Porperty quotient & power =log724-log7324=log724 324 power and product Power Property =log73+⅓log8=log73+log8⅓=log(73•8⅓)=log(73• √ 3 8 ) Use the properties of logarithms to condense each expression into asingle logarithm. There should be no + or - in your answer. Answer: log3( Properties of logarithms • ) Use the properties of logarithms to condense each expression into asingle logarithm. There should be no + or - in your answer. Answer: log8( Properties of logarithms • √ ) Use the properties of logarithms to condense each expression into asingle logarithm. There should be no + or - in your answer. Answer: log4( Properties of logarithms • √ ) Use the properties of logarithms to condense each expression into asingle logarithm. There should be no + or - in your answer. Answer: log6( Properties of logarithms ) Use the properties of logarithms to condense each expression into asingle logarithm. There should be no + or - in your answer. Answer: log8( Properties of logarithms ) Use the properties of logarithms to condense each expression into asingle logarithm. There should be no + or - in your answer. Answer: log7( Properties of logarithms ) Use the properties of logarithms to condense each expression into asingle logarithm. There should be no + or - in your answer. Answer: log8( Properties of logarithms • √ ) Use the properties of logarithms to condense each expression into asingle logarithm. There should be no + or - in your answer. Answer: log9( Properties of logarithms • ) Use the properties of logarithms to condense each expression into asingle logarithm. There should be no + or - in your answer. Answer: log3( Properties of logarithms ) Use the properties of logarithms to condense each expression into asingle logarithm. There should be no + or - in your answer. Answer: log2( 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 logarithms logb(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: logb(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 = = |