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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8.5 Properties of logarithms

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8 5 properties of logarithms

8.5Properties of logarithms

p. 493


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


Assignment pg 496 15 72 x 3 s and 80 85 all

Assignmentpg. 49615 – 72 x 3’s and80-85 all


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