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Quiz 3.2

Quiz 3.2. Write the log as an exponent. Evaluate the log without using your calculator. 4. 3.3 Properties of Logarithms. Date: ____________. Change of Base Theorem. log x . log a x . = . log a . OR. ln x . log a x . = . ln a . 1). 2). 1). 2). Evaluating Logarithms. log23 .

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Quiz 3.2

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  1. Quiz 3.2 • Write the log as an exponent. • Evaluate the log without using your calculator. 4

  2. 3.3Properties of Logarithms Date: ____________

  3. Change of Base Theorem log x logax = log a OR ln x logax = ln a

  4. 1) 2)

  5. 1) 2)

  6. Evaluating Logarithms log23 log523 = ≈ 1.948 log5 OR ln23 log523 = ≈ 1.948 ln5

  7. Other Examples log149 log3149 = ≈ 4.555 log3 log300 log7300 = ≈ 2.9312 log7

  8. u logb = logbu − logbv v Properties of Logarithms Let b, u, and v be positive numbers such that b ≠ 1. logbuv = logbu + logbv Product Property Quotient Property logbun = nlogbu Power Property

  9. 1) 2) 3)

  10. 1) 2) 3)

  11. Find the exact value of the logarithm.

  12. Use the properties of logarithms to simplify the given expression.

  13. Use the properties of logarithms to simplify the given expression.

  14. Use the properties of logarithms to simplify the given expression.

  15. 4x6 log4 y Write as the sum, difference, or product of logarithms. Simplify, if possible. = log44x6 – log4 y = log44 + log4x6 – log4 y = log44 + 6log4x– log4 y = 1 + 6log4x– log4 y

  16. 6 log7 x3y Write as the sum, difference, or product of logarithms. Simplify, if possible. = log76– log7 x3y = log76 −(log7x3 + log7 y) = log76 − (3log7x+ log7 y) = log76 − 3log7x− log7 y

  17. Write as the sum, difference, or product of logarithms. Simplify, if possible. log57x = log57+ log5 x = log57 + log5x½ = log57 + ½log5x

  18. Write as the sum, difference, or product of logarithms. Simplify, if possible. ½ x3y5 x3y5 loga = loga z z x3y5 = ½loga z = ½(loga x3+ loga y5 – logaz) = ½(3loga x+ 5logay – logaz)

  19. 5x6 log3 = 7 Condense the expression to the logarithm of a single quantity. log35 + 6log3x− log3 7 = log35 + log3x6 − log3 7 = log3(5x6) − log3 7

  20. Condense the expression to the logarithm of a single quantity. 3log8 x − 5log8 y+ log8 15 = log8x3 − log8 y5 + log8 15 x3 log8 = •15 y5 15x3 = log8 y5

  21. Condense the expression to the logarithm of a single quantity. 3log8 x − 5log8 y− log8 15 = log8x3 − log8 y5 − log8 15 x3 = log8 15y5

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