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lgbasallote

how to solve for \(T_m\) using a calculator? \[\huge \frac{\ln (\frac{40 - T_m}{70-T_m})}{5} = \frac{\ln (\frac{0.5}{70-T_m})}{35}\]

  • one year ago
  • one year ago

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  1. baddinlol
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    Is it a simple scientific calculator?

    • one year ago
  2. lgbasallote
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    yep

    • one year ago
  3. mukushla
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    isolate Tm (on the right hand side equation)

    • one year ago
  4. lgbasallote
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    hmm?

    • one year ago
  5. mukushla
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    u will have a equation like: Tm=f(Tm) enter an initial guess to save it in the Ans then enter f(Tm) in ur calculator with Ans instead of Tm then push the Ans Button repeatedly to converge

    • one year ago
  6. lgbasallote
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    wahhh i dont get you...go slow please :(

    • one year ago
  7. phi
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    you could use newton's method \[ y_{n+1}= y_n - \frac{f(y_n)}{f'(y_n)} \]

    • one year ago
  8. lgbasallote
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    wahh? o.O

    • one year ago
  9. lgbasallote
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    lol i only need to know how to input this in calculator :C

    • one year ago
  10. phi
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    I believe you can only find a solution using a numerical technique, an iterative search that converges on an answer. A bit painful using a calculator. If you just want the solution, use wolfram.

    • one year ago
  11. lgbasallote
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    but i need to learn howto use my calculator...hmm will you just tell me how to isolate tm then?

    • one year ago
  12. phi
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    you can get to a form like \[ 2(40-T_m)^7=(7-T_m)^6 \] but you can not isolate Tm...

    • one year ago
  13. lgbasallote
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    hmm...where did 2 come from again?

    • one year ago
  14. phi
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    *70 the 2 from 0.5

    • one year ago
  15. lgbasallote
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    oh og course

    • one year ago
  16. lgbasallote
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    of course*

    • one year ago
  17. lgbasallote
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    @phi are you familiar with the shift + solve in scientific calculators?

    • one year ago
  18. phi
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    No, but I assume it can solve equations numerically?

    • one year ago
  19. lgbasallote
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    i think so..if i can figure it out...

    • one year ago
  20. phi
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    maybe this will help for convenience, let y= 40-x, so the problem can be written as \[2y^7= (y+30)^6 \] \[ 2^{(1/6)}y^{(7/6)}-y-30 = 0 \] now you find the roots of this expression, and then find x= 40-y

    • one year ago
  21. lgbasallote
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    hmm i did not get that lol sorry...i'll try doing trial and error on my calculator now

    • one year ago
  22. phi
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    what calculator are you using? so I can look at its user manual

    • one year ago
  23. lgbasallote
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    canon f-788dx

    • one year ago
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