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