Question

Help with rearranging an equation?? (equation in next post as can't put funny symbols in)

Answer 1

\[A=B.e ^{-\alpha(5T)}\]

Rearranging for alpha

Answer 2

Okay so first thing here would be to divide through by B. \[\frac{ A }{ B }= e^{−α(5T)}\]Now one property of the exponential is that if you take the natural log of it, it is 1. So ln(e)=1, which allows us to do the following. \[\ln(\frac{ A }{ B })= \ln(e^{−α(5T)})\] A property of any logarithm is that \[\log(a^b)=blog(a)\]So we can take the power outside, and since ln(e) is 1, we have \[\ln(\frac{ A }{ B })= −α(5T)\ln(e)\] meaning \[\ln(\frac{ A }{ B })= −α(5T)\] now just divide by -5T and we get \[\frac{ -1 }{ 5T }\ln(\frac{ A }{ B })=α\]And we are done. Hope that this helped:)

Answer 3

You sir, are amazing. Thank you!