8.5 Properties of logarithms

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# 8.5 Properties of logarithms - PowerPoint PPT Presentation

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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### 8.5Properties of logarithms

p. 493

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 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 log53≈.683 and log57≈1.209
• Approximate:
• log549 =
• log572 =
• 2 log57 ≈
• 2(1.209)=
• 2.418
Expanding Logarithms
• You can use the properties to expand logarithms.
• log2 =
• log27x3 - log2y =
• log27 + log2x3 – log2y =
• log27 + 3·log2x – log2y
• Expand:
• log 5mn=
• log 5 + logm + logn
• Expand:
• log58x3 =
• log58 + 3·log5x
Condensing Logarithms
• log 6 + 2 log2 – log 3 =
• log 6 + log 22 – log 3 =
• log (6·22) – log 3 =
• log =
• log 8
• Condense:
• log57 + 3·log5t =
• log57t3
• Condense:
• 3log2x – (log24 + log2y)=
• log2
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:
• Use the change of base to evaluate:
• log37 =
• (base 10)
• log 7 ≈
• log 3
• 1.771
• (base e)
• ln 7≈
• ln 3
• 1.771