Clarifying Equation Rewriting Method

[Pietair]

Good day.

I want to rewrite the following equation:
$$0.5p_{ss}=p_{ss}(1-e^{\frac{Lp}{Ix}t})$$

What I do is:
$$ln(0.5)=ln(1)-ln(e^{\frac{Lp}{Ix}t})$$
$$ln(0.5)=-{\frac{Lp}{Ix}t}$$

Though in the notes received it says:
$$ln(0.5)={\frac{Lp}{Ix}t}$$ (without the minus sign)

Am I doing something wrong?

 

[HallsofIvy]

So you mean you have 0.5p_ss= p_ss(1- e^((Lp/Ix)t)) and you want to "rewrite the equation"? Rewrite it how? Solve the equation for p_ss or perhaps Lp or Ix or t?

You then have ln(0.5)= ln(1)- ln(e^((Lp/Ix)t)). How did you get that? Not by taking the logarithm of both sides of the first equation. That would be ln(0.5p)= ln(p_ss(1- e[sup[(Lp/Ix)t)[/sup]) which reduces to ln(0.5)+ ln(p)=ln(p)+ ln(1- e^((Lp/Ix)t)) and the "ln(p)" terms cancel to give ln(0.5)= ln(1- e^((Lp/Ix)t)) but ln(1- e^((Lp/Ix)t)) is NOT ln(1)- ln(e^{((Lp)/Ix)t)): in general ln(a- b) is NOT ln(a)- ln(b). If I new HOW you were trying to "rewrite" the equation, I might be able to suggest reducing before you take the logarithm.}

 

[Pietair]

Thank you for your answer, I want to solve the equation for t.

0.5pss= pss(1- e((Lp/Ix)t))

Is the same as:
0.5= 1- e((Lp/Ix)t)

Isn't it?

I don't know how to continue to solve the equation for t...

 

[Mark44]

Add -1 to both sides, multiply both sides by -1, and then take the natural log of both sides.

 

[Pietair]

That makes sense, thanks a lot!