## lgbasallote Group Title how to solve for $$T_m$$ using a calculator? $\huge \frac{\ln (\frac{40 - T_m}{70-T_m})}{5} = \frac{\ln (\frac{0.5}{70-T_m})}{35}$ 2 years ago 2 years ago

Is it a simple scientific calculator?

2. lgbasallote Group Title

yep

3. mukushla Group Title

isolate Tm (on the right hand side equation)

4. lgbasallote Group Title

hmm?

5. mukushla Group Title

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 Group Title

wahhh i dont get you...go slow please :(

7. phi Group Title

you could use newton's method $y_{n+1}= y_n - \frac{f(y_n)}{f'(y_n)}$

8. lgbasallote Group Title

wahh? o.O

9. lgbasallote Group Title

lol i only need to know how to input this in calculator :C

10. phi Group Title

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 Group Title

but i need to learn howto use my calculator...hmm will you just tell me how to isolate tm then?

12. phi Group Title

you can get to a form like $2(40-T_m)^7=(7-T_m)^6$ but you can not isolate Tm...

13. lgbasallote Group Title

hmm...where did 2 come from again?

14. phi Group Title

*70 the 2 from 0.5

15. lgbasallote Group Title

oh og course

16. lgbasallote Group Title

of course*

17. lgbasallote Group Title

@phi are you familiar with the shift + solve in scientific calculators?

18. phi Group Title

No, but I assume it can solve equations numerically?

19. lgbasallote Group Title

i think so..if i can figure it out...

20. phi Group Title

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 Group Title

hmm i did not get that lol sorry...i'll try doing trial and error on my calculator now

22. phi Group Title

what calculator are you using? so I can look at its user manual

23. lgbasallote Group Title

canon f-788dx