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Properties of Logarithms

Properties of Logarithms. Section 3.3. 3.3 PROPERTIES OF LOGARITHMS. Change of base formula: log a x = log b x / log b a = log x / log a = ln x / ln a Evaluate log 9 1043. log 10 1043 / log 10 9 log 1043 / log 9 3.1630 Evaluate using ln: log 9 1043.

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Properties of Logarithms

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  1. Properties of Logarithms Section 3.3

  2. 3.3 PROPERTIES OF LOGARITHMS Change of base formula: loga x = logb x / logb a = log x / log a = ln x / ln a Evaluate log9 1043. log10 1043 / log10 9 log 1043 / log 9 3.1630 Evaluate using ln: log9 1043. ln 1043 / ln 9 3.1630 Same!

  3. Properties of Logarithms: loga (uv) = loga u + loga v ln (uv) = ln u + ln v loga u/v = loga u – loga v ln u/v = ln u – ln v loga un = n loga u ln un = n ln u

  4. Write each log in terms of ln 2 & ln 3: • ln 6 ln (2 · 3) ln 2 + ln 3 • ln 2/27 ln 2 – ln 27 ln 2 – ln 33 ln 2 – 3 ln 3

  5. Verify that – log10 1/100 = log10 100 -log10 100-1 = -(-1) log10 100 = log10 100 = Expand each expression: • log4 5x3y log4 5 + log4 x3 + log4 y log4 5 + 3 log4 x + log4 y

  6. ln √3x – 5 7 ln (3x-5)1/2 7 ln (3x – 5)1/2 – ln 7 ½ ln (3x – 5) – ln 7 Condense each expression: • ½ log10 x + 3 log10 (x + 1) log x1/2 + log (x + 1)3 log [ √ x (x + 1)3]

  7. 2 ln (x + 2) – ln x ln (x + 2)2 – ln x ln (x + 2)2 2 • 1/3 [log2 x + log2 (x – 4)] 1/3 {log2 [x(x – 4)]} log2 [x(x – 4)]1/3 log23√ x(x – 4)

  8. Homework • Page 211-213 10-20 even, 35, 37-55 odd, 72, 74

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