Finding Logarithmic equations

  • Thread starter Cummings
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In summary, Hurkyl uploaded a question asking for the equations of a graph with an asymptote at x = 3. By using the points given, and the asymptote, he was able to find the equations of the other two points.
  • #1
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Well then i am new here and can tell i am going to spend quite some time here as well :)

I need some help with Finding Logarithmic/exponential equations from points on a graph.

In general, says my math book, you need 2 points on a graph to find 2 unknowns.

fair enough..i covered that all fine.
but now we have 3 unknowns..with 2 points and 1 asymptote

i know an asymptote is a line that the graph approaches but never meets...
i can therefore pick a point and with quite a large amount of accuracy say that that is the 3rd point
for example
say if the graph is traveling close to the asymptote, x = 3 at anything above y = 8 then i just pick a y value(above 8) and assume the x value to be 3.
and i would have a third point...i don't haveto get the answer to 100 decimal places so assuming the x value to be 3 would make quite an accurate answer.

anyways..i have uploaded the question for u to look at...its question 8
 

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  • #2
where is the problem?
 
  • #3
Hello Cummings, and welcome to the forums
In general, says my math book, you need 2 points on a graph to find 2 unknowns.
That is not totally right, it mostly depends on what variables you are talking about, and wether or not you know the family of the graph that is drawn.

but now we have 3 unknowns..with 2 points and 1 asymptote
Again, it depends, on the unknowns.
say if the graph is traveling close to the asymptote, x = 3 at anything above y = 8 then i just pick a y value(above 8) and assume the x value to be 3. I don't haveto get the answer to 100 decimal.
If this is everyday math, then (although i do not understand what is your problem about), yes.
But in math, you either have to take everything to be accurate, or you have to calculate the accuracy, and make sure it lies within the the range required by the problem.
anyways..i have uploaded the question for u to look at...its question 8
I am sorry, i don't seem to be able to find the file anywhere !

Try to make your question clearer, and i am sure we will be able to answer you better.
 
  • #4
Points aren't the only source of information.

For instance, in problem #8, you know what the asymptote of the graph is. You also know (I presume) how to find the asymptote of a logarithmic graph from its equation. You can use this knowledge in order to write one of the three equations you need to compute A, b, and c. (The other two equations come from the given points)
 
  • #5
https://www.physicsforums.com/attachment.php?s=&postid=18189

i uploaded it before..unless u can't see it...

its question 8...
the equation is Alog[base e](x-b)+c
and i have the points (4,9) and (8,-6) and the asymptote x = 3
I need to find A, b and c
 
  • #6
Got it.

So, 1st thing: What does the asymptote tell you?
Well, you know that ln(0)=[oo], so you can find b from that.

Next, you use the two points given to find the other two constants.

Can you try that? If you get stuck, post what you've got and we'll help.
 
  • #7
Hurkyl, your right...

if the asymptote is at X = 3 the graph has been moved 3 units to the right... the value of b is what moves it so b must be positive and b must equal 3.

now we have eliminated b..we can use the 2 given points and the new equation y = Alog[base e](x-3)+c to find the 2 remaining points.

case closed..thanks Hurkyl.
 

1. What is a logarithmic equation?

A logarithmic equation is an equation in which a variable appears in the exponent. It is the inverse of an exponential equation, and is used to solve for the value of the variable.

2. How do I solve a logarithmic equation?

To solve a logarithmic equation, you can use the properties of logarithms to rewrite the equation in a simpler form. Then, you can isolate the variable and solve for its value. It is important to check your answer by plugging it back into the original equation.

3. Can I graph a logarithmic equation?

Yes, you can graph a logarithmic equation by plotting points and connecting them with a smooth curve. The shape of the graph depends on the base of the logarithm, and it will never touch or cross the x-axis.

4. What are the common uses of logarithmic equations in science?

Logarithmic equations are commonly used in science to model natural phenomena such as population growth, radioactive decay, and sound intensity. They are also used in chemistry to calculate pH and in physics to calculate the intensity of earthquakes.

5. Are there any real-life applications of logarithmic equations?

Yes, logarithmic equations have various real-life applications, such as in finance, where they are used to calculate compound interest. They are also used in computer science and engineering for data compression and signal processing.

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