# Stuck doing parametric natural log graphs

• Witcher
In summary, you got stuck when you tried to solve for y using the logarithm rule for e-based logarithms and the fact that ##a^{bc}=(a^b)^c##.
Witcher
Homework Statement
I haven’t done logs in a few month and let alone with parametric graphs. I am having trouble with this problem. #35
Relevant Equations
X=e^t, y=e^3t
I got stuck when i eliminated the parameter.

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Witcher said:
I got stuck
in full sight of the harbour as they say in shipping language: ##y = e^{3\log x}## should remind you of something like ##e^{ab} = e^{ba}##

I use ##\log## for e based logarithms. Only engineers confuse e and 10, which is why they need ##\log## and ##\ln## .

You have $x= e^t$ and $y= e^{3t}= (e^t)^3$ so $y= x^3$. I don't see any reason to use logarithms.

Chestermiller, berkeman, Witcher and 1 other person
You can keep “e^t” and isolate t without using logrithms?

Witcher said:
You can keep “e^t” and isolate t without using logrithms?
Yes, because you don't need to isolate t. As has already been explained, ##e^{3t} = (e^t)^3##, so you can write y in terms of x, getting rid of the parameter t.

Witcher and berkeman
Witcher said:
Homework Statement:: I haven’t done logs in a few month and let alone with parametric graphs. I am having trouble with this problem. #35
Homework Equations:: X=e^t, y=e^3t

I got stuck when i eliminated the parameter.
Hello, @Witcher . I see that you've been a member for a couple of months, but why not give you a welcome?

You have been led to and/or given shorter ways to the answer, but your start was OK.

Recall that ##\ \ C\cdot \ln(x) = \ln(x^C) ##.

Apply that to ##\ \ 3(\ln(x)) ##, and proceed .

Last edited:
Witcher
I get it now but it wasn’t easy, my instinct was to Ln both sides when i seen the e

Thanks.

BvU
Witcher said:
I get it now but it wasn’t easy, my instinct was to Ln both sides when i seen the e.

Thanks.
As I mentioned, the path you started down was fine. It makes sense to work with the logarithm rules you may currently be studying and/or those rules you are most familiar with.

Carrying on from where you left off, (with ##\displaystyle y=e^{3(\ln(x))} ##):

You then have ##\displaystyle y=e^{\ln(x^3)} ##.

The final result follows immediately. (I hope.)

One can also use the fact that ##a^{bc}=(a^b)^c##.

## 1. What is a parametric natural log graph?

A parametric natural log graph is a type of graph that plots a logarithmic function against a parameter. In other words, both the x and y axes are determined by a single variable, rather than just the x-axis in a traditional graph. It is commonly used in scientific and mathematical analysis to show the relationship between two variables on a logarithmic scale.

## 2. How do I create a parametric natural log graph?

To create a parametric natural log graph, you will first need to determine the logarithmic function that you want to plot. Then, choose a range of values for your parameter and calculate the corresponding x and y values for each point on the graph. Finally, plot these points on a graph with a logarithmic scale for the y-axis.

## 3. What are the advantages of using a parametric natural log graph?

One of the main advantages of using a parametric natural log graph is that it allows you to easily visualize and analyze the relationship between two variables on a logarithmic scale. This can be especially useful when dealing with large ranges of values, as it allows for better comparison and identification of patterns.

## 4. What types of data are best represented using a parametric natural log graph?

A parametric natural log graph is best used when representing data that follows a logarithmic relationship. This can include data that exhibits exponential growth or decay, such as population growth, disease spread, or radioactive decay. It can also be useful for representing data with a large range of values, as mentioned previously.

## 5. Can I use a parametric natural log graph for non-scientific data?

While parametric natural log graphs are commonly used in scientific and mathematical analysis, they can also be used for non-scientific data. For example, they can be used to plot financial data, such as stock prices, that may follow a logarithmic pattern. However, it is important to ensure that a logarithmic relationship actually exists in the data before using this type of graph.

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