Solve this equation for x




Location: Sydney, NSW
Member since 28 January 2011
Member #: 823
Postcount: 6005

Folks,
Please solve this equation for x and let me know your answer:
x = 240.7263/(7.591386/log_{10}(67.04/6.116441)^{1})
Note: The 1 at the end is an exponent.
I get a result that does not agree with the textbook, but I may be making an error.




Location: Wangaratta, VIC
Member since 21 February 2009
Member #: 438
Postcount: 4337

Did you work out what was in the brackets first? Strange way of putting the equation? Almost looks like an escapee from a "slide rule" (got two)
log base 10 is the common logarithms.
Marc




Location: Melbourne, VIC
Member since 5 October 2009
Member #: 555
Postcount: 410

32.97
Ian
‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾
Cheers,
Ian




Administrator
Location: Greenwich, NSW
Member since 15 November 2005
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No result will come from me unfortunately. Equations were probably my weakest point in maths at school and maths was generally a subject I loathed apart from geometry.
‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾
A valve a day keeps the transistor away...




Location: Sydney, NSW
Member since 28 January 2011
Member #: 823
Postcount: 6005





Location: Melbourne, VIC
Member since 5 October 2009
Member #: 555
Postcount: 410

Hi GTC,
I will check my calculation, but it shouldn't be a difficult equation to solve. Also did it "inside out" with Excel. Could be interpretation of formula from the text. Can you email the actual text?
Cheers,
Ian
‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾
Cheers,
Ian




Location: Sydney, NSW
Member since 28 January 2011
Member #: 823
Postcount: 6005

Okay, image of text emailed. (two graphics).




Location: Melbourne, VIC
Member since 5 October 2009
Member #: 555
Postcount: 410

GTC,
The equation is open to various interpretations.
I intrepreted the exponent as log{(X)1} .... and being less than 1 ... yields a minus answer.
If the exponent is of the whole log function ie {log(X)}1 then I also get 30.4956.....
Treating the 1 as integer "minus 1" ..... doesn't help either.
Another possibility, besides the book being incorrect (and it wouldn't be the first time), is the interpretation of "10log". I would also assume 'log base 10', but other bases to logs are used.
Is the text specific about "log base 10"??
Cheers,
Ian
‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾
Cheers,
Ian




Location: Melbourne, VIC
Member since 5 October 2009
Member #: 555
Postcount: 410

Hey GTC,
Just got your second email ..... the book is correct .... 32.21.
The problem was with the interpretation of 1.
Calculation should be Tn/[{m/log(Pw/A)}1] ie subtract 1 from m/log(Pw/A) then divide into Tn
Log is base 10
I will email my spreadsheet ... see the last calculation.
Cheers,
Ian
‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾
Cheers,
Ian




Location: Sydney, NSW
Member since 28 January 2011
Member #: 823
Postcount: 6005

Much confusion for me! Many thanks for the worked example.
I see you mean to say 38.21 above.




Location: Melbourne, VIC
Member since 5 October 2009
Member #: 555
Postcount: 410

Yes, 38.21. May I ask what the temperature calculation is for? Just curious.
Ian
‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾
Cheers,
Ian




Location: Sydney, NSW
Member since 28 January 2011
Member #: 823
Postcount: 6005

It's supposed to allow calculation (within 1% accuracy) of dew point temperature without recourse to the psychometric chart. I now have to see how good it is with local data.




Location: Wangaratta, VIC
Member since 21 February 2009
Member #: 438
Postcount: 4337

The only way you get 38.21 is to treat 1 as minus 1
If you divide out that which is in the inner bracket its log is 1.0398. divide 7.59.... by that and subtract 1 you end up with 6.3 as the divisor so then you have 240.72... / 6.3
Marc




Location: Sydney, NSW
Member since 28 January 2011
Member #: 823
Postcount: 6005

Marcc, yes thanks, Ian set me straight on that in post #9 above.
All good now.




Location: Wangaratta, VIC
Member since 21 February 2009
Member #: 438
Postcount: 4337

Basically, if the formula was written properly, there would never have been an issue: Only a problem, the value of "X"



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