Exam 2-Austin Schlief

Exam 2-Austin Schlief

1. 4.5

   • Examples
     • 2^x=16
     • 3^x=15(7^x)
     • 3.2^x=35(2.6^x)

2. 4.1

   • logarithm base 10 of x is defined by log10x=y if and only if 10^y=x
     • Examples
       • log(base 2)8
       • log(base 5) 1/25
   • Laws of Logarithms
     • log(base a)1=0 We raise a to the exponent 0 to get 1
     • log(base a)a=1 We raise a to the exponent 1 to get a
     • log(base a)a^x=x We raise a to the exponent x to get a^x
     • a^log(base a)x=x log(base a)x is the exponent to which as must be raised to get x

3. 4.3

   • Each successive mark on the scale corresponds to multiplying by a fixed factor
   • pH Scale
     • pH=-log(H+)
       • The pH of tomato juice is 4.2. Find the hydrogen ion concentration.
       • The hydrogen ion concentration of cheddar cheese was measured to be
         • [H+]= 1.26*10^-6M Find the pH
   • Decibel Scale
     • B=10xlog(I/10^-12)
       • Find the decibel level of a .41 magnum if the intensity was measured at
         • 10^4.32W/m^2
   • Richter Scale
     • M=log(I/S)

4. 4.2

   • Laws
     • The logarithm of a product is the sum of the logarithms
       • log(base 3)9x
     • The logarithm of a quotient is the difference of the logarithms
       • log(12/n)
     • The logarithm of a power is the exponent times the logarithm of the base
       • log(base 7) 3d^5/7
   • Combine the given expression into a single logarithm
     • 5log(x+2)-3logx
   • Evaluate each expression without the use of a calculator
     • log(base 9)3+log(base 9) 27
   • Change of Base Formula
     • log(base b)x=log(base a)x/log (base a) b

5. 3.1

   • Example
     • A rumor is spreading across the campus that there will be no final exams for any of the classes that semester. Show exponential growth and linear growth

6. 3.2

   • Exponential Models: Comparing Rates

7. 3.3

   • Comparing Linear and Exponential Growth and Decay