Math

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...