Re: New to Mathematica

• To: mathgroup at smc.vnet.net
• Subject: [mg126386] Re: New to Mathematica
• From: Murray Eisenberg <murray at math.umass.edu>
• Date: Sun, 6 May 2012 03:23:32 -0400 (EDT)
• Delivered-to: l-mathgroup@mail-archive0.wolfram.com
• References: <jntga4\$2c\$1@smc.vnet.net> <201205050814.EAA22939@smc.vnet.net>

```First, perhaps folks were reluctant to respond because this looked like
it could be a homework exercise.

Second, you don't even have proper Mathematica syntax in your equation
relating x and k. Did you even try to read the documentation to learn
the very basics? For example, proper syntax for the equation would be:

(x/Log[x]) (1 + 1/Log[x]) == 108.2 + k

Function arguments must be enclosed in brackets, not parentheses, and
the equality is a doubled "=" sign. Moreover, your original expression

Third, the equation itself looks really nasty. Aside from the fact that
it mixes exact formulas with an approximate real (108.2), the left-hand
side is transcendental.

Fourth, the equation does not seem to uniquely define x as a function of
k! For example, form the difference between the two sides...

f[x_] := (x/Log[x]) (1 + 1/Log[x]) - 108.2 - k

... and plot f for, say, k = 2:

Plot[Evaluate[f[x] /. k -> 2], {x, 0.5, 2}, Exclusions -> {x == 1},
AxesOrigin -> {0, 0}, PlotRange -> {-5, 5}]

The graph crosses the x-axis twice. And indeed, if you use FindRoot with
initial guesses above and below 1, you'll see that this is so:

FindRoot[Evaluate[f[x] /. k -> 2], {x, 0.9}]
{x -> 0.916554}

FindRoot[Evaluate[f[x] /. k -> 2], {x, 1.1}]
{x -> 1.11137}

On 5/5/12 4:14 AM, J.Jack.J. wrote:
> On May 3, 9:40 am, "J.Jack.J."<jack.j.jep... at googlemail.com>  wrote:
>> Hi,
>>
>>   I only need it for one thing (as yet, anyway), and I wonder whether
>> someone can help me in step-by-step fashion to get what I want. I need
>> the solution to the following (I might make amendments to the values):
>>
>> "For any integer k, let r(k) be x such that
>>
>> (x/ln(x))*(1 + 1/ln(x)) = 108.2 + k)
>>
>> product (k = 0 to 3000) (1-1/r(k))"
>>
>> With many thanks in advance.
>
> Can nobody help me with this? Just for a Newbie?
> As most will realise, the first lines define my function and the
> product (k = 0 to 3000) (1-1/r(k))
> is my desired calculation. I need to know what inputs to use.
>
>

--
Murray Eisenberg                     murray at math.umass.edu
Mathematics & Statistics Dept.
Lederle Graduate Research Tower      phone 413 549-1020 (H)
University of Massachusetts                413 545-2859 (W)
710 North Pleasant Street            fax   413 545-1801
Amherst, MA 01003-9305

```

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