1) Write in exponential form. log 27 9 = x 3) Evaluate. Warm-Up 2) Write in logarithmic form. 5 x =...
Transcript of 1) Write in exponential form. log 27 9 = x 3) Evaluate. Warm-Up 2) Write in logarithmic form. 5 x =...
1) Write in exponential form.
log279 = x
3) Evaluate.
Warm-Up2) Write in logarithmic form.
5x = 2003
log2
1
84) Write the Equation that models this situation:
The current world population of Oompa-loompas is 7,986. If the Ooompa-loompa population grows steadily at a rate of 19% per year, what will their total population be in 10 years?
Properties of Logarithmsloga1 = 0
logaa = 1
logaax = x a xa xlog If loga x= loga y then x = y
because a0 = 1because a1 = a
loglog
loga xx
a 10
10
Change-of-Base
log ( ) log loga a auv u v
log log loga a a
u
vu v
log logan
au n u
Product Property
Quotient Property
Power Property
Remember Common Logarithm??
log10 Is the “common” logarithm
This is the LOG button on the calculator
Sometimes we’re lazy and we don’t even write the base…
log107 = log 7
Basic Properties of Logarithms1) loga1 = 0
2) logaa = 1
because a0 = 1
because a1 = a
a.) log5 1
a.) log3 3
Product Propertylog ( ) log loga a auv u v
= loga M + loga N1) loga MN
= logb A + logb T2) logb AT
= log M + log A + log T + log H3) log MATH
Express as a sum of logarithms.
Express as a single logarithm
557log = log5 (19*3)
Ex.4) log5 19 + log5 3
5) log C + log A + log B + log I + log N
= log CABIN
Use log53 = 0.683 and log57 = 1.209 to approximate…
Ex. 7
log5 (21)
= log5 3 + log5 7
= 0.683 + 1.209
= 1.892
= log5 (3*7)
Use log53 = 0.683 and log57 = 1.209 to approximate…
Ex. 3
= log5 3 - log5 7
= 0.683 - 1.209
= -0.526
log5
3
7
Use log53 = 0.683 and log57 = 1.209 to approximate…
Ex. 6
= log5 72
= 2(1.209)
= 2.418
log5 49
= 2 log5 7
Expand10
4
23log
•Simplify the division.
104 23log loga
•Simplify the multiplication of 4
10 104 23log log loga
•Change the radical sign to an exponent
1
210 104log log log 23a
•Express the exponent as a product
10 10
1
24 23log log loga
Ex. 8
Ex. Condense.
31
210 10log logx y log log103
10
12
x y
yx310log
2 2log( ) logx x log( ) logx x2 2
log( )x
x
2 2
9)
10)
log log103
10x y
Condense1
5log log log4a a ax y z
•Express all products as exponents
•Simplify the subtraction.
•Change the fractional exponent to a radical sign.
1
45log log loga a ayx z
45log log loga a ay zx
54log loga a
x zy
•Simplify the addition.
45
logazx
y
Ex 11
Ex. 1
Evaluate. Round to four decimal places.
log3 7 log
log10
10
7
3
Be careful about the parenthesis in the calculator…
log(7) / log(3)
= 1.7712