Isolate t from x(t)=vτ(1-e-t/τ) Homework

[zeromaxxx]

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!

 

[tiny-tim]

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]

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!