8 5 properties of logarithms
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8.5 Properties of logarithms. p. 493. Properties of Logarithms. Let b, u, and v be positive numbers such that b ≠1. Product property: log b uv = log b u + log b v Quotient property: log b u/v = log b u – log b v Power property: log b u n = n log b u. Use log 5 3 ≈.683 and log 5 7≈1.209.

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properties of logarithms
Properties of Logarithms
  • Let b, u, and v be positive numbers such that b≠1.
  • Product property:
  • logbuv = logbu + logbv
  • Quotient property:
  • logbu/v = logbu– logbv
  • Power property:
  • logbun = n logbu
use log 5 3 683 and log 5 7 1 209
Use log53≈.683 and log57≈1.209
  • Approximate:
  • log53/7 =
  • log53 – log57 ≈
  • .683 – 1.209 =
  • -.526
  • log521 =
  • log5(3·7)=
  • log53 + log57≈
  • .683 + 1.209 =
  • 1.892
use log 5 3 683 and log 5 7 1 2091
Use log53≈.683 and log57≈1.209
  • Approximate:
  • log549 =
  • log572 =
  • 2 log57 ≈
  • 2(1.209)=
  • 2.418
expanding logarithms
Expanding Logarithms
  • You can use the properties to expand logarithms.
  • log2 =
  • log27x3 - log2y =
  • log27 + log2x3 – log2y =
  • log27 + 3·log2x – log2y
your turn
Your turn!
  • Expand:
  • log 5mn=
  • log 5 + logm + logn
  • Expand:
  • log58x3 =
  • log58 + 3·log5x
condensing logarithms
Condensing Logarithms
  • log 6 + 2 log2 – log 3 =
  • log 6 + log 22 – log 3 =
  • log (6·22) – log 3 =
  • log =
  • log 8
your turn again
Your turn again!
  • Condense:
  • log57 + 3·log5t =
  • log57t3
  • Condense:
  • 3log2x – (log24 + log2y)=
  • log2
change of base formula
Change of base formula:
  • u, b, and c are positive numbers with b≠1 and c≠1. Then:
  • logcu =
  • logcu = (base 10)
  • logcu = (base e)
examples
Examples:
  • Use the change of base to evaluate:
  • log37 =
  • (base 10)
  • log 7 ≈
  • log 3
  • 1.771
  • (base e)
  • ln 7≈
  • ln 3
  • 1.771
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