logarithms let’s get it started!!! remember a logarithm is an exponent every time you are...
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Let’s Get It Started!!!TRANSCRIPT
Let’s Get It Started!!!
Remember A logarithm is an exponent
Every time you are working with logarithms, you can substitute the word exponent for logarithm,
The symbol for logarithm is log
What is written
log 3 9
What is said
log to the base 3 of 9or
log base 3 of 9
What does it mean????What does it mean????
log log 3 3 99
meansmeans
what power of 3 is 9?what power of 3 is 9?
log log 33 9 = 2 9 = 2 becausebecause 3 3 22 = 9 = 9
^̂ ^ ^ logarithmic formlogarithmic form exponential form exponential form
Write in exponential form:Logarithmic Formlog 2 8 = 3
log 6 36 = 2
log 4 1 = 0
log 2 32 = 5
Exponential Form2 3 = 8
6 2 = 36
4 0 = 1
2 5 = 32
Write in logarithmic form
Exponential Form
3 0 = 1
5 4 = 625
10 -1 = .1
6 3 = 216
Logarithmic Form
log 3 1 = 0
log 5 625 = 4
log 10 (.1) = -1
log 6 216 = 3
Special log valueslog a 1 = 0 because
log a a = 1 because
log a a x = x because
a 0 = 1
a 1 = a
a x = a x
We interrupt the lesson on logarithms to We interrupt the lesson on logarithms to bring you an important message…bring you an important message…
Hold on!! Hold on!! Let’s make sure you Let’s make sure you understand what “if and understand what “if and only if” means.only if” means.
A triangle is scalene if and only if the triangle has 3 sides of different lengths.
The above statement takes the place of 2 statements:
A triangle is scalene if it has 3 sides of different lengths.
AND
A triangle with 3 sides of different lengths is scalene.
Now back to the lesson on logarithms…
DefinitionThe logarithm of x with base a (a > 0) is denoted bylog a x and is defined as
y = log a x iff a y = x
if and only if
y = log a x
Replace the y with f (x) and you have a function
f ( x ) = log a x
Evaluate:
log 5 25 =
log 4 64 =
log 2 64 =
log 4 2 =
log 3 (-1) =
2
3
6
½
Impossible Why????
The log function with base 10 is called the common log function
Your calculator uses base 10 when doing logarithms.
If using common logs, you do not need to write in the base of 10.
log 100 = 2
because 10 2 = 100
If you have any other base, to use your calculator, you can use the CHANGE OF BASE FORMULA:
log a x = log x / log a
Use your calculator to evaluate:
log 4 7 =
log 7 / log 4 1.404
Log 3 40 = log 40 / log 3
3.358
More Examples using the calculator
log 3 543 =
log 4 84 =
log 2 79 =
log 543 / log 3 5.732
log 84 / log 4 3.196
log 79 / log 2 6.304
Graph f ( x ) = log 2 x
Make a table of values
11 0022 1133 1.61.644 2288 33.5.5 -1-1.25.25 -2-2
x y
Let’s review logarithms
A logarithm is an exponent
Calculators use base 10
To find log 5 399, using a calculator, use log 399 / log 5 ( 3.72)
The End!
HOMEWORK TIME!!!