Question 172999: For the exponential function e^x and logarithmic function log x, graphically show the effect if x is doubled, can someone help me with the problem, I do not understand what they are asking. Thank you!!!
Found 2 solutions by stanbon, gonzo:
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! For the exponential function e^x and logarithmic function log x, graphically show the effect if x is doubled,
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e^x vs. e^(2x)
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ln(x) vs ln(2x)
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Comment:I can't get this site to graph ln(x) and ln(2x) which is ln(x) + ln(2)
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Cheers,
Stan H.
Answer by gonzo(654) (Show Source):
You can put this solution on YOUR website! they want to know the impact of doubling x.
i take this to mean:
if you have  and you double x, then you have 
likewise:
if you have  and you double x, then you have 
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first i will graph and to see what the impact would be:
look below the graph for further comments.
the faster rising curve is
when x = 0, the values of both curves is the same.
when x = 1, the value of is 2.718... and the value of is 7.389...
when x = 2, the value of is 7.389... and the value of is 54.598...
the value of  appears to be the value of  which is should since equals  by the laws of exponentiation.
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when x = -.5, = .6065 and = .3678.
 = .3678 so the ratio holds even though is smaller than at this point.
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you can see this on the graph.
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the graph of and is shown now.
look below the graph for further comments.
this graph doesn't show such a dramatic change in the value of log(x) versus log(2x)
example:
when x = 10, log(x) = 1, and log(2x) = 1.301...
when x = 100, log(x) = 2, and log(2x) = 2.301...
when x = 1000, log(x) = 3, and log(2x) = 3.301...
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this is because when x is an exponent, it has a very large impact on the result.
when x is the result of exponentiation, it has a very small impact on the result.
when x is the exponent, this is what happens:
if you take x = 1, then 10^1 = 10
if you take x = 10, then 10^10 = 10000000000
there's a big difference.
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when x is the result of exponentiation, this is what happens:
if you take x = 1000, then 10^y = 1000 which means y = 3.
if you double x to be 2000, then 10^y = 2000 which means y = 3.301029996
doubling the answers causes a very small increase in the exponent.
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y = 10^x means x is the exponent
y = log(x) means x is the answer.
remember:
y = log(x) if and only if x = 10^y
x is the result of exponentiation when you say y = log(x)
x is the exponent itself when you say y = 10^x.
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best i can do.
hope it makes sense.
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