# A quick question.

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? What do they have in relation? ]

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

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? 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

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

DonAntonio
Why is it the same?

MarneMath
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.

Mark44
Mentor
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.