What are the steps in these differential equations?

This image is hard to read, but I

*think* the steps were as follows:

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\(\displaystyle \mbox{1. }\, \dfrac{dM}{S\, -\, kM}\, =\, dt\)

\(\displaystyle \mbox{2. }\, -\dfrac{1}{k}\, \ln(S\, -\, kM)\,\big|_0^t\, =\, t\,\big|_0^t\)

\(\displaystyle \mbox{3. }\, \left(-\dfrac{1}{k}\right)\, \ln\left(\dfrac{S\, -\, km(t)}{S\, -\, km(0)}\right)\, =\, t\)

\(\displaystyle \mbox{4. }\, M(t)\, =\, M(0)\, e^{-kt}\, +\, \dfrac{S}{k}\, \left(1\, -\, e^{-kt}\right)\)

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When you say that you don't understand these steps (which involve nothing past what you learned back in algebra and in calculus), please clarify what you mean. For instance, you should understand how they got the log expression in step (3), because you understand how log rules work, and how you can convert a subtraction containing two logs into one log containing a division.

Please be specific. Thank you!