Finding Logarithmic equations

Cummings

Well then i am new here and can tell i am going to spend quite some time here aswell :)

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 dont 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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dav2008

Gold Member
where is the problem?

STAii

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 dont 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.

Hurkyl

Staff Emeritus
Gold Member
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)

Cummings

https://www.physicsforums.com/attachment.php?s=&postid=18189

i uploaded it before..unless u cant 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

Tom Mattson

Staff Emeritus
Gold Member
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.

Cummings

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.

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