i need to derive a logarithmic equation in the form y=aloge(x+b)+c

given that it passes through the points (0,0) (12,20) (30,30)

it is a positive log with a horizontal asymptote x<0

can someone please help me work it out cos it is difficult!!!!!!!

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- May 27th 2006, 06:49 PMasian5logarithmic equation from points
i need to derive a logarithmic equation in the form y=aloge(x+b)+c

given that it passes through the points (0,0) (12,20) (30,30)

it is a positive log with a horizontal asymptote x<0

can someone please help me work it out cos it is difficult!!!!!!! - May 27th 2006, 07:18 PMThePerfectHackerQuote:

Originally Posted by**asian5**

Subsituting this into this equation yields,

---------

From equation 1 we have,

Substitute that into equation 2 and 3 thus,

Thus,

Divide these equation thus,

Cross multiply,

Now raise to that power,

Thus,

Thus,

Open sesame,

Thus,

Thus,

<to be countinued>

this gives you b. - May 27th 2006, 07:48 PMThePerfectHacker
In the previous post I gave you the analytic method, I do not know if you care for that but simply for a solution.

If you want that then,

And it gives you this curve below with the points bolded. - May 28th 2006, 01:27 AMasian5finish please
thanks so much,

but would u b able to finish the working from the quadratic for "b" u came up with, and sub that value back into the approapriate equation to find the other values. correct to three decimal places

thanks - May 28th 2006, 02:01 AMCaptainBlackQuote:

Originally Posted by**ThePerfectHacker**

Thus,

Thus,

which has roots , and if we want

and to be real this rules out the first of these

roots and so , which is reassuringly in agreement

with the numerical result.

RonL - May 28th 2006, 02:16 AMasian5finish
did you use the quadratic formula?

what equation do i sub this 'b' value into to give 'a' and 'c'? correct to 3 decimal places? - May 28th 2006, 02:33 AMCaptainBlackQuote:

Originally Posted by**asian5**

Substitute the value of into any two of the three equations

given at the top of The PerfectHackers first post, say:

this will leave you with a pair of linear equations in and .

or:

.

RonL - May 28th 2006, 02:47 AMasian5
now do u solve similtaneously?

can u take me through it please - May 28th 2006, 04:35 AMCaptainBlackQuote:

Originally Posted by**asian5**

so:

Substituting this back into the first of the equations gives:

so:

RonL - May 28th 2006, 10:46 AMThePerfectHacker
Thank you CaptainBlack for finishing my post, saved me a lot of time.

- May 28th 2006, 10:50 AMCaptainBlackQuote:

Originally Posted by**ThePerfectHacker**

RonL