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3.3B Expand & Condense Properties

3.3B Expand & Condense Properties. Common Logs Base of a. Natural Logs. l n ( uv ) = lnu + lnv ln = lnu – lnv ln = nlnu -------------------Condense More pieces to fewer All pieces MUST have same base in order to condense. ( uv ) = u + v = u - v = n u

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3.3B Expand & Condense Properties

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  1. 3.3B Expand & Condense Properties Common Logs Base of a Natural Logs ln(uv) = lnu + lnv ln = lnu – lnv ln = nlnu -------------------Condense More pieces to fewer All pieces MUST have same base in order to condense. • (uv) = u + v • = u - v • = nu • Expand ------------- • Fewer pieces to more • Each piece will have same base after expanded.

  2. Examples: • 1. Write ln6 in terms of ln2 and ln3. • 2. Write ln in terms of ln2 and ln3. • 3. Write ln20 in terms of ln4 and ln5.

  3. Examples: Expand • 4. 5y • 5. ln • 6. (# 53) ln()

  4. Examples: Condense • 7. x + 3(x+1) • 8. 2ln(x+2) – lnx • 9. [x + (x-4)]

  5. Example: Condense • 10. (# 71) lnx – 2[ln(x+2) + ln(x-2)]

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