Chapter 4

Chapter 4

1. A is positive then Log Base a=logax=y

   • Logarithmically equation: 5^4=625
     • log5(625)=4

2. exponential functions and logarithmic functions are inverses

   • Smaller number=fractional exponent

3. Change of Base Formula

   • logb=logxX/logab
   • log11(355)=x.....11^x=355

4. Subtraction=Divide, Add=Multiply

   • Sum=logb(mn)=logb(m)+logb(n)
     • Difference=lobb(m/n)=logb(m)-logb(n)
       • Exponent=logb(m^n)=n*logb(m)
         • log7(3d^5/7)=log7(3)+5log7(d)-1
       • log(12/n)=log(12)-log(n)
     • log3(9x)= 2+log3(x)

5. Combining logarithm

   • log(j)+log(k)=log(jk)

6. Natural Exponential function: f(x)=e^x

   • Exponential Model: f(x)=Ca^x
     • Exponential Function: f(t)=Ce^rt
       • Exponential growth:(r>0)
         • Exponential decay:(r<0)

7. natural logarithm function: f(x0-In(x)=loge(x)

   • In(1)=loge(1)=x=e6x=1,=0

8. Instantaneous growth rate is expressed as a proportion of the population per time limit

9. Exponent----------Log

10. pH Scale: pH=log[H+]

    • Above 7=basic
      • PH=-log[H+]
        • EX: [H+]=3.16X 10^-8M
          • pH= -log[3.16x10^-8]= 7.5 basic

11. Decibel Scale: S=k*log (I/I0)

    • Richter Scale: M=log(I/S)

12. Compound Pr^rt

    • Compound Monthly : P(1+r/)^nt

13. Log===exponent

    • IN====E