# Understanding Logarithm Functions: f(x) = log(100x)

• nesan
In summary, we discussed the concept of logarithms and a specific function, f(x) = log(100x), which can be rewritten as f(x) = logx + log100 = logx + 2. This function represents both a compression towards the y-axis by a factor of 100 and a vertical translation up by 2 units. Both interpretations are essentially the same and just represent different ways of looking at the same thing.
nesan
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. >_<

nesan said:
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

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

DonAntonio

Why is it the same?

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.

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.

## What is a logarithm function?

A logarithm function is the inverse of an exponential function. It is used to solve for the exponent in an exponential equation. In other words, if the exponential equation is y = a^x, then the logarithm function is expressed as x = loga(y).

## What is the base of a logarithm function?

The base of a logarithm function is the number that is raised to a certain power in order to get a specific value. In the function f(x) = loga(b), "a" is the base, "b" is the value, and "x" is the exponent.

## What is the domain of a logarithm function?

The domain of a logarithm function is all positive real numbers. This means that the input (x) must be greater than 0 in order for the function to be defined and have a real output.

## What is the range of a logarithm function?

The range of a logarithm function is all real numbers. This means that the output (y) can be any real number, including negative numbers.

## How do you graph a logarithm function?

To graph a logarithm function, you can use the properties of logarithms to determine key points on the graph, such as the x-intercept and y-intercept. You can also plot points by choosing values for x and solving for y. Additionally, you can use a graphing calculator or online graphing tool to visualize the function.

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