# Math Help - simple simplification

1. ## simple simplification

Im just confused as to how this step (1) [ -ln l 150 - y l = (t / 200) - ln 130 ], simplified into this (2) l 150 - y l = 130e^(-t/200)

The only part i dont understand about this is how (t/200) in (1) became (-t/200) in (2)

Thanks

2. Originally Posted by johntuan
Im just confused as to how this step (1) [ -ln l 150 - y l = (t / 200) - ln 130 ], simplified into this (2) l 150 - y l = 130e^(-t/200)

The only part i dont understand about this is how (t/200) in (1) became (-t/200) in (2)

Thanks
Note that $-\ln\left|150-y\right|=\frac{t}{200}-\ln 130\implies \ln\left|150-y\right|=-\frac{t}{200}+\ln 130$

So $\left|150-y\right|=e^{-\frac{t}{200}+\ln 130}=e^{-\frac{t}{200}}e^{\ln 130}=130e^{-\frac{t}{200}}$

Does this make sense?