Stuck doing parametric natural log graphs

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##.
  • #1
Witcher
15
3
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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  • #2
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}##

[edit]I use ##\log## for e based logarithms. Only engineers confuse e and 10, which is why they need ##\log## and ##\ln## :smile: .
 
  • #3
You have [itex]x= e^t[/itex] and [itex]y= e^{3t}= (e^t)^3[/itex] so [itex]y= x^3[/itex]. I don't see any reason to use logarithms.
 
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  • #4
You can keep “e^t” and isolate t without using logrithms?
 
  • #5
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.
 
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  • #6
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?
:welcome:

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

1575243617464.png


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

Apply that to ##\ \ 3(\ln(x)) ##, and proceed .
 
Last edited:
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  • #7
I get it now but it wasn’t easy, my instinct was to Ln both sides when i seen the e

Thanks.
 
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  • #8
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.)
 
  • #9
One can also use the fact that ##a^{bc}=(a^b)^c##.
 

Related to Stuck doing parametric natural log graphs

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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