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March 19, 2018
x log x12345678910
Round to thousandths
log 3 + log 5 log (3*5)log 2 + log 8 log (2*8)log 9 + log 6 log (9*6)
8.4 d10
log 1=0 log ,o10=XProperties Bol
of -477 10=10a 602
Logs :399g 10=1.
845.903.1954
b-
=. 477.699=1%1*77%8⇐ log 152 I. 176
a-→ == .
9541=778--1.732
A >OB > o
←addition
log At log B = logCAB)Same base
March 19, 2018
Based on your findings on the previous pageComplete the following statement:
Now, make a conjecture.
log ( Min ) Product
Property.
Quotientlog IFu) Property
March 19, 2018
Properties of Logarithms
Product Property
Quotient Property
Power Property
Seeprevious Page
.
f
log ME x log M
These properties can be appliedto logarithms of any base
March 19, 2018
State the property or properties used to rewrite each expression
' ' o
?⇐ z
→ T.ge#=logz2
→
FFsaBtBB¥¥¥; property
'
;¥Ilogs czpyrgduotproperty
March 19, 2018
Write each logarithmic expression as a single logarithm
⇒¥÷÷÷
iasmmm÷÷÷÷÷÷÷"
3 logb
4 - 3 logy 2-
3 log ,22 - 3 log
,2
610%2 - 3 log ,2
= I
310%2 = log,
23 -- logy,
8
d
→ 3 log ,Xt
loggywrite as a" ¥::::::::④ 10%641Apply the power propertybefore applying the
Product or Quotient Properties
March 19, 2018
Expand each logarithm
(a) = log,
a' Flog,b "=3 log ,
at 410g,b
= log 27 t log zb
°=log y②- log32=2 logy - log 9I
+ \ 2 log1=2 (logy - logs)T = 2 logy -2 log 3
March 19, 2018
Loudness of Sounds
L=,'¥I - intensityof sound in
Io a lowest intensity sound for a human
[ = loudness ofsound findB )
March 19, 2018
-
=LI
,= present intensity
Iz=.5i÷:::÷:
:÷*h=m'¥Lz = reduced loudness 12=10 log II *
µ 4 - La = change in dB Io
- e ←
to log- 10 log 'I÷ → 1010g '¥ - blog
- -
loflog log !I÷)→10 (log -- lofog
HOClog # )=lO( log 2)
March 19, 2018carotene,
T O r
"
-
- .
IT log Z - I, log
3 - I log X
log Z"4 - log 344 - log x
"
-
log ,) -log x
"
= log IFE- log x
5k
log = log HE. x - 5h )T log ¢"
4 j ki ×- 5h )
March 19, 2018
a,eMEEq¥ ajog, ④t log ,
IIsi: '
i'
" ÷÷÷ .
March 19, 2018E¥e = log
log X - logy
I 109×4 ttzlogxy - 3log×Z ¥1091logy
109×4"
+ log ,,Yk - logxz'
109×2+109×442 - log ×Z'
logy @y" ) - log ,,Z
'
log , )
March 19, 2018Expand3
iI
= logs U"
- log,
WV"
=3 log su - ( logs W t logsV " )=3 log su - logs.
w - 4 logs V
'"'
logs 42 - 9
iE-Hlogs 5 - logs 24
I - log 524 pmI - logs (6 - 4) =/ - Cogs.Gt logs4)
I - I. I -
.9 he - I
March 19, 2018
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