Transcript Example - Mr.Zuccheroso

Properties Continued
5 – Product Law:
logcmn = logcm + logcn
Simplify:
log310 + log32
log3(10.2)
log3(20)
log20 = 2.73
log3
Example
Solve for x:
log22 + log25 = x
log2(2x5) = x
log210 = x
log10 = x
log2
3.32 = x
6 – Quotient Law:
logc(m/n) = logcm - logcn
Simplify:
log25 – log23
log2(5/3)
log(5/3) = 0.74
log2
Example
Solve for x: log333 - log311 = x
log3(33/11) = x
log33 = x
x=1
Example
Solve for x: log296 - log23 = x
log2(96/3) = x
log232 = x
2x = 32
x=5
7 –Law of Powers:
logcmn = nlogcm
Simplify:
xlog28x
x2log2(8)
x2log(8) = 3x2
log2
Example
Simplify:
log243
3log24
3(2)
(since log24=2)
6
Example
Simplify:
log2 3√7
= log27⅓
= ⅓log27
= ⅓(2.81)
= 0.94
Example
log7493
= 3log749
= 3(2)
(since log749=2)
=6
8 – Change of Base Law:
logcx = logx
(we already know this one!)
logc
Example
7x = 400
log7400 = x
x = log400
log7
x = 3.07
Examples:
Simplify each expression into a single logarithm:
a) log4 – 2log8
b) 5lny -3lnx
c) log2x + (logy – log4)
d) 2(log2x – logy) – (log3 + 2log5)
e) 2log3 + log2 – log6 – log4
f) 3lny -2lny2 + lny3
a) log4 – 2log8
b) 5lny -3lnx
c) log2x + (logy – log4)
d) 2(log2x – logy) – (log3 + 2log5)
e) 2log3 + log2 – log6 – log4
f) 3lny -2lny2 + lny3