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lgbasallote

  • 2 years ago

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

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  1. baddinlol
    • 2 years ago
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    Is it a simple scientific calculator?

  2. lgbasallote
    • 2 years ago
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    yep

  3. mukushla
    • 2 years ago
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    isolate Tm (on the right hand side equation)

  4. lgbasallote
    • 2 years ago
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    hmm?

  5. mukushla
    • 2 years ago
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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

  6. lgbasallote
    • 2 years ago
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    wahhh i dont get you...go slow please :(

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

  8. lgbasallote
    • 2 years ago
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    wahh? o.O

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

  10. phi
    • 2 years ago
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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.

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

  12. phi
    • 2 years ago
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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...

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

  14. phi
    • 2 years ago
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    *70 the 2 from 0.5

  15. lgbasallote
    • 2 years ago
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    oh og course

  16. lgbasallote
    • 2 years ago
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    of course*

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

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

  19. lgbasallote
    • 2 years ago
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    i think so..if i can figure it out...

  20. phi
    • 2 years ago
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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

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

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

  23. lgbasallote
    • 2 years ago
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    canon f-788dx

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