Math3-S2-Demo8_Logarithm.mw

Math 3 Winter 2004

Introduction to Calculus


Class Demo for the Laws of Logarithms

March 1, 2004


   Choose some a and compare ln(x) with ln(ax)

> a := 3.:
for x from 1. to 3. by 0.25 do
 print(ln(x), ln(a * x), ln(a * x) - ln(x)):
od:

0., 1.098612289, 1.098612289

.2231435513, 1.321755840, 1.098612289

.4054651081, 1.504077397, 1.098612289

.5596157879, 1.658228077, 1.098612289

.6931471806, 1.791759469, 1.098612288

.8109302162, 1.909542505, 1.098612289

.9162907319, 2.014903021, 1.098612289

1.011600912, 2.110213200, 1.098612288

1.098612289, 2.197224577, 1.098612288

   Compare this with ln(a)

> ln(a);

1.098612289

   And now the graph of ln(x)

> plot(ln('x'), 'x' = 0..10, y = -5..5);

[Plot]

>