Exponential & Logarithmic Functions

Exponential & Logarithmic Functions

1. Solving

   • Key Info:
     • To solve, make bases of both sides of the equation the same, and then work with just the exponents.
       • When this cannot be calculated properly, use common logarithms to solve the equation. Apply the power, quotient, or product law in order to find the correct answer.
       • Example:
   • Essentially finding the "x's" of the equation. Isolate the x so it is alone.
   • NOTE: At times you will eed to use the quadratic formula to solve the problems.

2. Laws of Logarithms

   • Power Law
     • Ex.
   • Product Law
     • Ex.
   • Quotient Law
     • Ex.

3. Basic Exponential Laws

   • Power Law: (a^b)^c = a^bc
   • Product Law: a^b * a^c = a^(b+c)
   • Quotient Law: a^b / a^c = a^(b-c)

4. Graphing

5. Different Scales

   • pH Scale:
   • Richter Scale:
   • Decibel Scale

6. Equations that can help with problem solving questions.

   • Half life: A(t)=A.(1/2)^t/h
     • In which: A. = inital value, t=time, h=half-life time, A(t) is final amount.
   • Doubling Time: A(t)=A.(2)^t/d
     • In which A.=inital value, t=time, d=doubling time, and A(t) is final amount.

7. Problem-Solving Word Problems (APPLICATION)

   • Ex. 1
   • Ex. 2
   • Ex.3

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