lgbasallote
how to solve for \(T_m\) using a calculator?
\[\huge \frac{\ln (\frac{40 - T_m}{70-T_m})}{5} = \frac{\ln (\frac{0.5}{70-T_m})}{35}\]
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baddinlol
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Is it a simple scientific calculator?
lgbasallote
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yep
mukushla
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isolate Tm (on the right hand side equation)
lgbasallote
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hmm?
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
lgbasallote
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wahhh i dont get you...go slow please :(
phi
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you could use newton's method
\[ y_{n+1}= y_n - \frac{f(y_n)}{f'(y_n)} \]
lgbasallote
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wahh? o.O
lgbasallote
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lol i only need to know how to input this in calculator :C
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.
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?
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...
lgbasallote
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hmm...where did 2 come from again?
phi
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*70
the 2 from 0.5
lgbasallote
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oh og course
lgbasallote
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of course*
lgbasallote
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@phi are you familiar with the shift + solve in scientific calculators?
phi
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No, but I assume it can solve equations numerically?
lgbasallote
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i think so..if i can figure it out...
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
lgbasallote
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hmm i did not get that lol sorry...i'll try doing trial and error on my calculator now
phi
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what calculator are you using? so I can look at its user manual
lgbasallote
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canon f-788dx