Question

how to solve for \(T_m\) using a calculator?

\[\huge \frac{\ln (\frac{40 - T_m}{70-T_m})}{5} = \frac{\ln (\frac{0.5}{70-T_m})}{35}\]

Answer 1

Is it a simple scientific calculator?

Answer 2

yep

Answer 3

isolate Tm (on the right hand side equation)

Answer 4

hmm?

Answer 5

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

Answer 6

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

Answer 7

you could use newton's method

\[ y_{n+1}= y_n - \frac{f(y_n)}{f'(y_n)} \]

Answer 8

wahh? o.O

Answer 9

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

Answer 10

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.

Answer 11

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

Answer 12

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

Answer 13

hmm...where did 2 come from again?

Answer 14

*70

the 2 from 0.5

Answer 15

oh og course

Answer 16

of course*

Answer 17

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

Answer 18

No, but I assume it can solve equations numerically?

Answer 19

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

Answer 20

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

Answer 21

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

Answer 22

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

Answer 23

canon f-788dx