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 graphs of logarithims
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bounce
Junior Member

Azerbaijan
3 Posts

Posted - 05/14/2007 :  20:04:59  Show Profile  Reply with Quote
this is a basic concept and i can clearly see that the results are different but the theory of it eludes me, maybe because i used a calculator.......
A machine design student noted that the edge of a robotic link was shaped like a logarithmic curve. Using a a graphing calculator the student viewed various logarithmic curves including y=log x
and y= 2log x, for which the student thought would be identical, but a difference was observed, write a paragraph explaining the difference and why it occurs.

now the graphs exhibit 2 different trends, for y = log x
it appears that it exists for all negative and positive values of y
for y= 2logx it seems that it only exists for all positive values of y.
but according to the text i'm studying they should be proportional to eachother and therefore have the same values, so why the difference in the graphs?
any help here would be greatly appreciated
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Subhotosh Khan
Advanced Member

USA
9116 Posts

Posted - 05/15/2007 :  07:25:02  Show Profile  Reply with Quote
quote:
Originally posted by bounce

this is a basic concept and i can clearly see that the results are different but the theory of it eludes me, maybe because i used a calculator.......
A machine design student noted that the edge of a robotic link was shaped like a logarithmic curve. Using a a graphing calculator the student viewed various logarithmic curves including y=log x
and y= 2log x, for which the student thought would be identical, but a difference was observed, write a paragraph explaining the difference and why it occurs.

now the graphs exhibit 2 different trends, for y = log x
it appears that it exists for all negative and positive values of y
for y= 2logx it seems that it only exists for all positive values of y.
but according to the text i'm studying they should be proportional to eachother and therefore have the same values, so why the difference in the graphs?
any help here would be greatly appreciated



This is because in reality

log(x2) = 2 * log(|x|)

|x| = absolute value of x

log(x) is not defined in the real domain for negative x.

Just like (x) is not defined in the real domain for negative x.

thus

The graph of y = (x)2 is not identical to the graph of y = x
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bounce
Junior Member

Azerbaijan
3 Posts

Posted - 05/15/2007 :  23:25:34  Show Profile  Reply with Quote
quote:
Originally posted by Subhotosh Khan

quote:
Originally posted by bounce

this is a basic concept and i can clearly see that the results are different but the theory of it eludes me, maybe because i used a calculator.......
A machine design student noted that the edge of a robotic link was shaped like a logarithmic curve. Using a a graphing calculator the student viewed various logarithmic curves including y=log x
and y= 2log x, for which the student thought would be identical, but a difference was observed, write a paragraph explaining the difference and why it occurs.

now the graphs exhibit 2 different trends, for y = log x
it appears that it exists for all negative and positive values of y
for y= 2logx it seems that it only exists for all positive values of y.
but according to the text i'm studying they should be proportional to eachother and therefore have the same values, so why the difference in the graphs?
any help here would be greatly appreciated



This is because in reality

log(x2) = 2 * log(|x|)

|x| = absolute value of x

log(x) is not defined in the real domain for negative x.

Just like (x) is not defined in the real domain for negative x.

thus

The graph of y = (x)2 is not identical to the graph of y = x

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bounce
Junior Member

Azerbaijan
3 Posts

Posted - 05/15/2007 :  23:28:10  Show Profile  Reply with Quote
quote:
Originally posted by Subhotosh Khan

quote:
Originally posted by bounce

this is a basic concept and i can clearly see that the results are different but the theory of it eludes me, maybe because i used a calculator.......
A machine design student noted that the edge of a robotic link was shaped like a logarithmic curve. Using a a graphing calculator the student viewed various logarithmic curves including y=log x
and y= 2log x, for which the student thought would be identical, but a difference was observed, write a paragraph explaining the difference and why it occurs.

now the graphs exhibit 2 different trends, for y = log x
it appears that it exists for all negative and positive values of y
for y= 2logx it seems that it only exists for all positive values of y.
but according to the text i'm studying they should be proportional to eachother and therefore have the same values, so why the difference in the graphs?
any help here would be greatly appreciated



This is because in reality

log(x2) = 2 * log(|x|)

|x| = absolute value of x

log(x) is not defined in the real domain for negative x.

Just like (x) is not defined in the real domain for negative x.

thus

The graph of y = (x)2 is not identical to the graph of y = x



thank you so very much for clarifying that for me.

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