exponents help

[Toots]

Can anyone help me rearrange this equation to help find the answer to t

N=(K*B*(exp(rt))/(K+(B*exp(rt)-1))

 

[Toots]

I am finding it difficult to rearrange given the exponents in the equation. Please can you help me rearrange this equation so I can find t = ?

N = (K*B*exp(rt))/(K+(B*(exp(rt)-1)))

 

[tkhunny]

Make a useful substitution. Maybe [math]M = Be^{rt}[/math], and solve first for M. See if that helps.

 

[Paul Belino]

Simplify by a substitution.
For example let X = exp(rt).
Now you just have N = (k*x)/(k + (x-1)).
Make X the subject and it boils down to X = (N-K)/(N-K) = 1
So X = 1, now replace with X = exp(rt) and then take LOG base e of boths sides of equals sign.
Now make t the subject, job done.