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Type of paper: Coursework
Subject area: Mathematics
Academic level: High school, College, Bachelor
Style: MLA
Size: 40.0 kB
Word count:
678 words/3 pages
Mark awarded:  
Author: Mercy Alvarez
Date submitted: 2008-11-21 19:41:36
Rating/Votes count:
5.00 / 2
 
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Tags: home, word, values, study, example, math, functions, influences, exponential, Norwegian, Figure, Logarithmic Functions, Simulation Setup, Start Simulation
Logarithmic Functions
A . In 30-50 words , describe which property of logarithms you find most
striking give three different examples of how and when the property is
used and explain its importance thoroughly .
Equation 1 The most striking property of the logarithms is the one shown in
equation 1 . For example loge (ex x loge (e ) and since loge (e 1 , then
loge (ex x . Another example is in simplifying the log10 (10x x
log10 (10 ) and since log10 (10 1 , then loge (ex x . This is important in
simplifying . These are important in simplifying equations of the form
loga (ax . Another example is the application of the above property in
programming to evaluate the exponent of any number xa . Normally there is
no existing function for the exponent of any number but the exponent of
the natural log (loge (x ln (x ) is usually available . So from from
ln (xa a ln (x ) we get xa ex ln (x .
B . Write a one page (250 word ) summary on how to graph exponential
functions of the form , b any positive , zero or negative number , or .
Include 6 representative examples .
y bx
Graphing exponential functions requires a good understanding of their
behavior . By their nature , the points in an exponential function tend
either to be very close to one fixed value or else to be too large to be
conveniently graphed . So generally there will only be a few points that
are reasonable to plot for drawing your picture . Because exponentials
change in y by a given proportion over a set period of x , means that for
a certain fixed change in x the value could half or double . The higher
the value of b for y bx , the faster the value of y changes as you vary
the value of x . You start by evaluating smaller values of exponent x
from a certain small negative number say for example -4 , then increment
x by 1 until it becomes 4 . Normally this range would give you a
sufficiently enough number of points to plot . See the example shown
below for y 2x . Also sometimes when you are using a calculator to
tabulate the values of an exponential function , sometimes the values of
y would appear to be always zero at certain numbers , but these does not
mean that they are really zero , but rather they are too small for the
calculator to represent in numbers . For example in figure 1 , the values
for y from -4 to -2 appears to lie on the axis where y 0 but they are
just too small to be differentiated graphically .
C . Write a one page (250 word ) summary on how to graph logarithmic
functions of the form , b any positive , zero or negative number , or .
Include 6 representative examples .
y loge (x ln (x )
To graph logarithmic functions "by hand , we need first to remember that
logs are not defined for negative x or for x 0 , so we do not need to
find points...
 

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