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Mastering Logarithm Condensation: Overview and Practice

This lesson provides an essential review of condensing logarithmic expressions and understanding the change of base formula. Through a series of examples and exercises, we illustrate how to condense various log expressions, such as transforming 2log2x + log2y into log2(x²y) and applying properties of natural logarithms. Students will gain practice through targeted homework exercises and learn crucial techniques to simplify log expressions efficiently, preparing them for more complex calculations.

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Mastering Logarithm Condensation: Overview and Practice

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  1. TODAY IN pRECALCULUS • Go over homework • Notes: • Condensing Log Expressions • Change of Base formula • Homework

  2. Condensing Log Expressions Example: condense: log5x - log5y Example: Condense: 2log2x+log2y = log2x2+log2y = log2x2y Example: Condense: 3lnx + 4 ln(y+4) =lnx3 + ln(y+4)4 =lnx3(y+4)4

  3. Example: condense: 4[lnz + ln(z+5)] – 2ln(z-5) = 4[lnz(z+5)] – 2ln(z-5) = ln[z(z+5)]4 – ln(z-5)2

  4. Practice condense: log3x + log37 7log8(x+4) 2[3log4x + log4(x+1)-log4(x-1)] log10x + 2log10y - 3log10z lnx – 4[ln(x+2) + ln(x-2)]

  5. log3x + log37 = log37x 7log8(x+4) = log8(x+4)7 2[3log4x + log4(x+1)-log4(x-1)] = 2[log4x3 + log4(x+1)-log4(x-1)]

  6. log10x + 2log10y - 3log10z =log10x + log10y2 - log10z3= lnx – 4[ln(x+2) + ln(x-2)] = lnx – 4[ln(x+2)(x-2)] = lnx – ln[(x+2)(x-2)]4

  7. Change of Base Formula • Allows us to rewrite logs in terms of base 10 or e so we can calculate the value of the log.

  8. Example =2.404 • Find the value log428 • Rewrite log8x as a ratio of both common and natural logs

  9. Homework • Page 317: 13-22all, 23-35odd

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