### May 24th Scribe By Marcquin

Well lets see here... Todays first class in morning we began with some questions.

**Write as an expontial**

a) log

_{2}64 = 6

64 = 2

^{6}

b) log

_{7}343 = 3

343 = 7

^{3}

**Write as a logarithm**

a) 3

^{8}= 6561

log3

^{6561}= 8

b) 25

^{3/2}= 125

log

_{25}125 = 3/2

**Evaluate:**

a) log

_{2}4

^{3/2}

log2(2

^{2})3/2

log

_{2}2

^{3}

b) 5log

_{5}

^{10}= 10

**Solve:**

log

_{t}4 = 2

2

^{2}= t

^{2}

2 = t

**Expand**

log

_{2 (m3 n5)1/2 = 3/2 log2m+ 5/2 log2nbring down the 1/2, therefore1/2 log2 (m3 n5)Remember "power of a power"log2 (m3/2 n5/2)multiply the exponentslog2m3/2 + log2n5/2Given: log5 = 0.70 log2 = 0.30without using a calculator find log 0.08Start of by saying 0.08 = 8/100If you look at the number it can be simplified to 2/25You must use a power to get a power which will get you 2/ 52Answer: log 0.08 = log (2/52)0.08 = log 2/52= log 2 - 2 log5= 0.30 - 2 (0.70)= 0.30 - 1.40= - 1.10Solve: logax + loga(x-2) = loga3logax(x-2) = loga3x2-2x = 3x2-2x-3 = 0(x-3) (x+1) = 0x=3 Acceptx=-1 RejectWe also had a talk about the population question in class. I am sorry guys because I lost the notes for it.Journal NotesEXPONENTS AND LOGARITHMSExponential Function: Any function where the variable is an exponent written in the form}

_{}

_{}

_{}

_{f(x) = abTHE ROLE OF PARAMETER Aa determines the y-intercept of the function a.k.a. the initial value (i.e. x=0) of the function.a<0>the graph is reflected in the y-axis THE ROLE OF PARAMETER Bb is the base of the exponential functionb is also known as the multiplication factor.b>1 the function is increasing. This is known as "exponential growth".0the function is decreasing. This is known as "exponential decay".LOGARITHMSDefinition: 1) A logarithm is a function that turns a power into an exponent.2) The logarithmic function, logba = c, is the inverse of the exponential function bc = a where b does not equal zero and a>0.logb a = cb is the basea is the argumentc is the logarithmwhich meansbc = ab is the basea is the powerc is the exponentExamples: log381 = 4 means 34 = 81log232 = 5 means 25 = 32log4 (1/16) = -2 means 4-2 = 1/16log51/125 = -3 means 5-3 = 1/125log100 = 2 means 102 = 100}

^{GRAPHICALLY}

^{Since the logarithm function is the inverse of the exponential function...}

**Remember: A logarithm is an exponent!**

**LAWS OF LOGARITHMS**__Product law__: log

_{a}mn = log

_{a}m + log

_{a}n

*Example: log*

_{2}(4 * 32) = log_{2}4 + log_{2}32__Quotient law__: log

_{a}(m/n) = log

_{a}m - log

_{a}n

*Example: log*

_{3}(81/27) = log_{3}81 - log_{3}27

__Power law__: log_{a}m^{b}= b log_{a}m*Example: log*

_{5}25^{3}= 3 log_{5}^{25}__Change of base law__: log

_{a}m = log

_{b}

^{m}all over log

_{b}

^{a}

*Example: log*

_{8}^{4}= log_{2}^{4}all over log_{2}^{8}

__SPECIAL CASES:__1) log

_{a}a = 1

2) log

_{a}1 = 0

3) log

_{a}a

^{x}= x

4)

_{a}log a

^{x}= x

__The Common Logarithm__

A logarithm function to the base 10 ( log

_{10}x) is called a "common logarithm". This base is so frequently used that it is simply written as log x, without the base indicated.

When no base is indicated, base 10 is assumed.

**THE NATURAL LOGARITHM**e = 2.718281828459...

e is a number that arises naturally in the study of exponential functions, particularly in the case of continuous exponential growth. The natural logarithm function is written as:

lnx i.e. log

_{e}x = lnx

read as "el-en of x"

And thats the whole bottle of wax for today!

So I will end off with a joke, haha just joking guys. So the next scribe has to be jan. It was inevitable!

## 2 Comments:

Nice Scribe Post. You are continuting the excellent scribbing going on in this class. Your choice of font for your definitions could be larger. I am having a hard time reading it. If you change your font this would be ready for the Hall of Fame.

Mr. Harbeck

Sargent Park School

This is an

outstandingscribe post Marquin! Take Mr. H's advice and then we can induct you into the Scribe Post Hall of Fame!Post a Comment

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