Properties of Logarithms
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logb Let b, u, and v be positive numbers such that b ≠ 1. Here, b can be any positive numbers other than 10. u and vmultipliedtogether Product Property u v 乘變加 = logb add exponents u + logb v Properties of logarithms logb Quotient Porperty u and vdivided u v = logb 除變減 u subtract exponents - logb v u to apower logb Power Property 連乘變連加 u n = n multiply exponents logb u    Estimate the following logarithm WITHOUT using a calculator. log556 = log5(7•8)= log57 + log58≈ 1.2 + 1.3≈ 2.5 Product Property Properties of logarithms = log712 - log710≈ 1.3 - 1.2≈ 0.1 Quotient Porperty log7 12 10 log364 = log382 = 2•log38 ≈ 2•1.9 ≈ 3.8 Power Property  Estimate the following logarithm WITHOUT using a calculator. Answer: Properties of logarithms Hint: Go back to the previous page.  Estimate the following logarithm WITHOUT using a calculator. Answer: Properties of logarithms  Estimate the following logarithm WITHOUT using a calculator. Answer: Properties of logarithms  Estimate the following logarithm WITHOUT using a calculator. Answer: Properties of logarithms Remember: log51 = 0  Estimate the following logarithm WITHOUT using a calculator. Answer: Properties of logarithms  Estimate the following logarithm WITHOUT using a calculator. Answer: Properties of logarithms  Estimate the following logarithm WITHOUT using a calculator. Answer: Properties of logarithms  Estimate the following logarithm WITHOUT using a calculator. Answer: Properties of logarithms Remember: log91 = 0  Estimate the following logarithm WITHOUT using a calculator. Answer: Can you make 36 two different ways? Do you get the same answer either way? :) Properties of logarithms Answer (yes/no):  Estimate the following logarithm WITHOUT using a calculator. Answer: Properties of logarithms    Often there are a combination of properties in one question. Expand the followings. No powers or radicals in your answer. = log9x2 + log7y4 = 2•log9x + 4•log7y product & power Product Property Properties of logarithms = log7x16 - log7y4 =16•log7x - 4•log7y quotient & power Quotient Porperty = log5z2 + log5x½= 2•log5z + ½•log5x = 2•log5z + power and product Power Property log5x 2  Expand the followings. No powers or radicals in your answer. Answer: log8 Properties of logarithms + log8 Hint: Go back to the previous page. answers should be in orderof increasing logs.i.e log6x+log6y+log6z not log6z+log6y+log6xnot log6y+log6x+log6z  Expand the followings. No powers or radicals in your answer. Answer: log7 Properties of logarithms + log7 answers should be in orderof increasing logs.i.e log6x+log6y+log6z not log6z+log6y+log6xnot log6y+log6x+log6z  Expand the followings. No powers or radicals in your answer. Answer: log6 + log6 Properties of logarithms + log6 answers should be in orderof increasing logs.i.e log6x+log6y+log6z not log6z+log6y+log6xnot log6y+log6x+log6z  Expand the followings. No powers or radicals in your answer. Answer: log2 Properties of logarithms - log2  Expand the followings. No powers or radicals in your answer. Answer: log9 Properties of logarithms - log9  Expand the followings. No powers or radicals in your answer. Answer: log9 Properties of logarithms - log9  Expand the followings. No powers or radicals in your answer. Answer: log + log Properties of logarithms + log Hint: log(u•v•w)½ = ½log(u•v•w) Then write as a fraction.  Expand the followings. No powers or radicals in your answer. Answer: log2 Properties of logarithms + log2  Expand the followings. No powers or radicals in your answer. Answer: log3 Properties of logarithms + log3  Expand the followings. No powers or radicals in your answer. Answer: log7 + Properties of logarithms log7    Often there are a combination of properties in one question. Simplify the followings. No + or - in your answer. Product Property =log8(u⅓•v⅓•w⅓)=log8( product & power √ 3 u•v•w ) Properties of logarithms Quotient Porperty quotient & power =log7x3-log7y2=log7x3 y2 power and product Power Property =log5c3+½log5a=log5c3+log5a½=log5(c3•a½)=log5(c3• √ a )  Simplify the followings. No + or - in your answer. Answer: log5( Properties of logarithms • )  Simplify the followings. No + or - in your answer. Answer: log4( Properties of logarithms • √ )  Simplify the followings. No + or - in your answer. Answer: log9( Properties of logarithms )  Simplify the followings. No + or - in your answer. Answer: log2( Properties of logarithms )  Simplify the followings. No + or - in your answer. Answer: log4( Properties of logarithms )  Simplify the followings. No + or - in your answer. Answer: log4( Properties of logarithms • )  Simplify the followings. No + or - in your answer. Answer: log6( Properties of logarithms )  Simplify the followings. No + or - in your answer. Answer: log( Properties of logarithms )  Simplify the followings. No + or - in your answer. Answer: log4( √ 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: logb(a) = Properties of logarithms log(b) log(a)  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 = =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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