Transcript Condense: 2log 2 x+log 2 y = log 2 x 2 +log 2 y = log 2 x 2 y

TODAY IN pRECALCULUS
• Go over homework
• Notes:
• Condensing Log Expressions
– Change of Base formula
• Homework
Condensing Log
Expressions
Example: condense: log5x - log5y
 log 5
x
y
Example: Condense: 2log2x+log2y
= log2x2+log2y
= log2x2y
Example: Condense: 3lnx + 4 ln(y+4)
=lnx3 + ln(y+4)4
=lnx3(y+4)4
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
 ln
 z  z  5  
 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)]
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)]
 x ( x  1) 
 x ( x  1) 
 2 log 4 
  log 4 

 x 1 
 x 1 
3
3
2
log10x + 2log10y - 3log10z
2
xy
=log10x + log10y2 - log10z3=log 10 3
z
lnx – 4[ln(x+2) + ln(x-2)]
= lnx – 4[ln(x+2)(x-2)]
= lnx – ln[(x+2)(x-2)]4
 ln
x
  x  2   x  2  
4
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.
change of base form ula : log a x 
for base 10 : log a x 
for base e : log a x 
log x
log a
ln x
ln a
log b x
log b a
Example
• Find the value log428

log 28
=2.404
log 4
OR 
ln 28
 2.404
ln 4
• Rewrite log8x as a ratio of both common and
natural logs
log 8 x 
log x
log 8
log 8 x 
ln x
ln 8
Homework
• Page 317: 13-22all, 23-35odd