Chapter 4

Chapter 4

1. Logarithms Base a

   • log a^x =y only if a^y = x
   • Change of base formula
     • logb^x = loga^x/loga^b

2. Laws of logarithms

   • logb (mn) = logb (m) + logb (n)
     • logb (m/n) = logb (m) - logb (n)
       • logb (m^n) = n * logb (m)

3. logarithmic scales

   • Linear scale: Each successive mark on the scale corresponds to adding a fixed #
     • Logarithmic scale: Each successive mark on the scale corresponds to multiplying by a fixed factor
       • Logarithmic scales are used to convert extremely large # into reasonable #
   • The pH Scale
     • pH = log[H^*], where [H^+] in the ions in a solution
     • decible scale
       • s = k * log (I/I^0)
       • Richter scale
         • M = log (I/S)

4. e^x and ln (x) are inverses

   • Natural Exponential function
     • f (x) = e^x
       • natural Logarithm function
         • f (x) = ln (x) = loge (x)
   • Exponential growth and decay
     • f (t) = Ce^rt