Need help re-arranging (a refresher on logs)!

Question

amtran_bus · Answer

attachment

amtran_bus · Answer

I know to kick the ln out I need to do the inverse, e.

photon336 · Answer

so for starters here's how we can re-write this 

$$Ln[\frac{ [A] }{ [A_{0}] } = Ln[A]-Ln[A_{0}]$$

$$Ln\frac{ x }{ y } = \ln(x)-\ln(y)$$

photon336 · Answer

for this actually we would take the e^ of both sides

photon336 · Answer

we can easily apply the above identity 

$$\ln([A])-Ln(A_{0}) = -kt $$

photon336 · Answer

Then afterwards we take the e of everything 

$$e^{\ln{A}}-e^{\ln{a0}} = e^{-kt}$$

$$[A]-[A_{0}] = -e^{-kt}$$

anthonyym · Answer

How I remember it is the base to the power of what's on the other side of the equation equals the number (what it's the log of). 
For example, log base 2 of 8 = 3.
2^3 = 8

amtran_bus · Answer

Thank you so much @Photon336 Sorry I was not here when you did that!!!!!!

photon336 · Answer

yeah absolutely no problem that's the half life equation FYI