A quick question.

  • Thread starter nesan
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  • #1
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We're learning logarithms in school. I asked my teacher this question but she couldn't explain it very well.

For a function such as f(x) = log(100x), base ten of course.

When graphed I could say the graph is "compressed by a factor of 1 / 100"

or

Rewriting f(x) = log(100x) into f(x) = logx + log100 = logx + 2

Now it's f(x) = logx + 2

which is a vertical translation up two units. Why is it both? o_O

What do they have in relation? ]

Please and thank you, just want to understand this. >_<
 

Answers and Replies

  • #2
606
1
We're learning logarithms in school. I asked my teacher this question but she couldn't explain it very well.

For a function such as f(x) = log(100x), base ten of course.

When graphed I could say the graph is "compressed by a factor of 1 / 100"

or

Rewriting f(x) = log(100x) into f(x) = logx + log100 = logx + 2

Now it's f(x) = logx + 2

which is a vertical translation up two units. Why is it both? o_O

What do they have in relation? ]

Please and thank you, just want to understand this. >_<

It is not both: it is the same as the graph of log x but translated two units.

DonAntonio
 
  • #3
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It is not both: it is the same as the graph of log x but translated two units.

DonAntonio
Why is it the same?
 
  • #4
MarneMath
Education Advisor
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I think you just showed why it's the same. Think of as the number 5. 4 + 1 = 5, 3 + 2 = 5, there can be two ways to write the same number, and in much the same way we can write some functions in multiple ways.
 
  • #5
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If you take any point (x, y) on the graph of y = log(x), you'll see that there is a point (x/100, y) on the graph of f(x) = log(100x), so one way of looking at the graph of f is that it represents a compression toward the y-axis of the graph of y = log(x) by a factor of 100.

On the other hand, the same point (x, y) on the graph of y = log(x) corresponds to the point (x, y + 2) on the graph of y = log(x) + 2, so this version of the function represents a translation up by 2 units.

Although log(100x) ##\equiv## log(x) + 2, we're looking at two different transformations, one in the horizontal direction, and one in the vertical direction. All we are doing is looking at one thing in two different ways.
 

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