# Isolate for Time

## 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

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tiny-tim
Science Advisor
Homework Helper
welcome to pf!

hi zeromaxxx! welcome to pf!
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! )

HallsofIvy
Science Advisor
Homework Helper

## 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:
$$e^{-t/\tau}= 1- \frac{x(t)}{v_T}$$

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!