Chapter 3 Map

Chapter 3 Map

1. Logs

   • Graphing Logs
     • Horizontal Shift Dilation Reflection Vertical Shift
     • Log x base 3= y X Y 3 1 9 2 1 0 1/3 1
   • Evaluating Logs
     • Log 1 base 3 Same as: 3^x=1 Answer=0
     • Log 6 base 8+/- Log 6 base 8 Addition is multiply Log 36 base 8 Subtraction would be divide Log 1 base 8 Exponent goes before 2 Log 6 base 8
     • Different base: Log 7 base 2/ Log 7 base 3 Solution: (Log 7/Log2)/(Log 7/ Log 3)
   • y = loga x
   • Using Logs to solve functions
     • Example: $600=$400(1.025)^t Log(1.5)/Log(1.025)=t

2. Exponentials

   • Graphing Exponentials
     • Horizontal Shift Reflection Dilation Vertical Shift
     • Y=2(3)^x-1 Y int: 2/3 Graph moves right 1
   • Evaluating Exponentials
     • 2=2(3)^x Same as:1=3^x X=0
   • f(x)=ab^x
   • Creating exponential functions
     • Example: You invest $400 at 2.5% compounded annually for t years.
       • A=$400(1+0.025)^t
       • Example: $400 is compounded continuously at 0.025% A=$400e^(1.025t)

3. Equations on left and right side are inverse of each other.

   • Log 3 base 1= 0 3^0= 1