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Example: condense: 4[lnz + ln(z+5)] – 2ln(z-5)
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TODAY IN PRECALCULUS•Go over homework•Notes: (no handout, need a
calculator)•Condensing Log Expressions
– Change of Base formula•Homework
Condensing Log ExpressionsExample: condense: log5x - log5y
Example: Condense: 2log2x+log2y
Example: Condense: 3lnx + 4 ln(y+4)
Example: condense: 4[lnz + ln(z+5)] – 2ln(z-5)
condense: log3x + log377log8(x+4)2[3log4x + log4(x+1)-log4(x-1)]log10x + 2log10y - 3log10zlnx – 4[ln(x+2) + ln(x-2)]
Practice
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.
log: loglog
ba
b
xchange of base formula xa
log10 : loglogaxfor base xa
ln: loglnaxfor base e xa
Example• Find the value log428
• Rewrite log8x as a ratio of both common and natural logs
Homework• Page 317: 13-22all, 23-35odd
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)]
3
4( 1)2 log
1x xx
23
4( 1)log
1x xx
log10x + 2log10y - 3log10z=log10x + log10y2 - log10z3=
2
10 3log xyz
lnx – 4[ln(x+2) + ln(x-2)] = lnx – 4[ln(x+2)(x-2)]
= lnx – ln[(x+2)(x-2)]4
42 2
xlnx x
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