Isolate for Time

  • Thread starter zeromaxxx
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  • #1
zeromaxxx
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Homework Statement


I just need to isolate t from the equation though I'm stumped on how to do it.

Homework Equations



x(t) = vτ(1-e-t/τ)

*τ and v are constants

The Attempt at a Solution


I know you somehow need to take the ln of both sides so

ln x(t)/vτ = ln (1-e-t/τ)

That's pretty much where I got to so far. Any suggestions on how to proceed to the next steps will be appreciated. Thanks!
 

Answers and Replies

  • #2
tiny-tim
Science Advisor
Homework Helper
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welcome to pf!

hi zeromaxxx! welcome to pf! :smile:
x(t) = vτ(1-e-t/τ)

*τ and v are constants

I know you somehow need to take the ln of both sides …

yes, "somehow" is the important word …

the trick is to get the e on its own on one side, and everything else on the other …

then you have ln(e) on one side, which is simple

(and not ln(1 - e)), which is useless! :wink:)
 
  • #3
HallsofIvy
Science Advisor
Homework Helper
43,021
970

Homework Statement


I just need to isolate t from the equation though I'm stumped on how to do it.

Homework Equations



x(t) = vτ(1-e-t/τ)

*τ and v are constants

The Attempt at a Solution


I know you somehow need to take the ln of both sides so

ln x(t)/vτ = ln (1-e-t/τ)
Too soon! First isolate the exponential by (1) subtract 1 from both sides, (2) multiply both sides by -1:
[tex]e^{-t/\tau}= 1- \frac{x(t)}{v_T}[/tex]

NOW take the natural logarithm of both sides.


That's pretty much where I got to so far. Any suggestions on how to proceed to the next steps will be appreciated. Thanks!
 

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