Eliminating logarithms?

Question

I'm learning to work with logarithms, and am having problems isolating the I in ln(I).

Here is the initial problem: I need to solve for I
ln(I) - ln(I0) = -kx

The 0 in ln(I0) is a little 0 similar to the base in a non-base-10 log, but I have no idea what that means.

Thanks!

Answer 1

just to keep things straight, let's use b instead of l, and a instead of l sub 0. The 0 subscript means initial value -- it's a before and after relationship here. So

ln b - ln a = -kx
ln (b/a) = -kx
b/a = e^(-kx)
b = a•e^(-kx)

which is your basic exponential decay equation. replace b with l and a with l sub 0.

Answer 2

Subtraction of logs = log of the division

→ ln(I/I0) = -kx
→ I/I0 = e^(-kx)
→ I = I0 * e^(-kx)