Chapter 4

Chapter 4

1. 4.1

   • log a x=y
     • a^y=x
       • log 9 (729)= 3
         • 9^3=729
     • 5^4=625
       • log 5 (625)=4
   • inverses reflect over graph
   • change of base formula
     • log a x/log a b
   • base of a log= reaches height of 4

2. 4.2

   • expanding logs
     • log 3 (9x)
       • log 3 (9) + log 3 (x)
         • 2 + log 3 (x)
           • 3^2= 9
         • x = +
     • log (12/n)
       • log 10 (12) - log 10 (n)
       • / = -
   • condensing logs
     • log (j) +log (k)
       • log (jk)
     • log 6 (1512)- log 6 (7)
       • log 6 (1512/7)
         • log 6 (216)
           • 3
           • what exponent gets 6 = 216

3. 4.3

   • use log scale for accuracy
     • take log of #
   • B=10Xlog(I/10^-12)

4. 4.4

   • natural expo. function = f(x)= e^x
     • natural log. function= f(x)= ln(x)= log e (x)
   • f(x)= Ce^rt = instantaneous

5. 4.5

   • make the log an exponential function, then solve