## lgbasallote 3 years ago how to solve for $$T_m$$ using a calculator? $\huge \frac{\ln (\frac{40 - T_m}{70-T_m})}{5} = \frac{\ln (\frac{0.5}{70-T_m})}{35}$

Is it a simple scientific calculator?

2. lgbasallote

yep

3. mukushla

isolate Tm (on the right hand side equation)

4. lgbasallote

hmm?

5. mukushla

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

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

7. phi

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

8. lgbasallote

wahh? o.O

9. lgbasallote

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

10. phi

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

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

12. phi

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

13. lgbasallote

hmm...where did 2 come from again?

14. phi

*70 the 2 from 0.5

15. lgbasallote

oh og course

16. lgbasallote

of course*

17. lgbasallote

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

18. phi

No, but I assume it can solve equations numerically?

19. lgbasallote

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

20. phi

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

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

22. phi

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

23. lgbasallote

canon f-788dx