Quiz 3.2. 3.3 Properties of Logarithms Date: ____________

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Transcript of Quiz 3.2. 3.3 Properties of Logarithms Date: ____________

3.3 Properties of Logarithms

Quiz 3.23.3Properties of LogarithmsDate: ____________Change of Base Theoremlogax = log x log a logax = ln x ln a OR1)

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5Evaluating Logarithmslog523 = log23 log5 1.948ORlog523 = ln23 ln5 1.948Other Exampleslog3149 = log149 log3 4.555log7300 = log300 log7 2.9312Properties of LogarithmsProduct PropertyQuotient PropertyPower PropertyLet b, u, and v be positive numbers such that b 1.logbuv = logbu + logbvlogbun = nlogbulogb = logbu logbvuv1)

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10Find the exact value of the logarithm.

Use the properties of logarithms to simplify the given expression.

Use the properties of logarithms to simplify the given expression.

Use the properties of logarithms to simplify the given expression.

Write as the sum, difference, or product of logarithms. Simplify, if possible. log4 4x6y=log44x6 log4 y = log44 + log4x6 log4 y = log44 + 6log4x log4 y = 1 + 6log4x log4 y Write as the sum, difference, or product of logarithms. Simplify, if possible.log7 6x3y=log76 log7 x3y= log76 (log7x3 + log7 y) = log76 (3log7x + log7 y) = log76 3log7x log7 yWrite as the sum, difference, or product of logarithms. Simplify, if possible.log57 x = log57 + log5 x= log57 + log5x= log57 + log5x

Write as the sum, difference, or product of logarithms. Simplify, if possible.loga x3y5

z = loga x3y5 z = loga x3y5 z = (loga x3+ loga y5 logaz) = (3loga x+ 5loga y logaz) Condense the expression to the logarithm of a single quantity.log35 + 6log3x log3 7= log35 + log3x6 log3 7 = log3(5x6) log3 7 = log3 7 5x6Condense the expression to the logarithm of a single quantity.3log8 x 5log8 y + log8 15= log8x3 log8 y5 + log8 15 15 log8y5=x3 = log8y515x3x3Condense the expression to the logarithm of a single quantity.3log8 x 5log8 y log8 15= log8x3 log8 y5 log8 15 = log815y5