10.2 Outline

A.  Fundamental properties
      1. logarithmic equation
      2. Grant's tomb properties
           a. x is the exponent on a base b that gives b^x.
           b. log_bx is the exponent on a base b that gives x.
B. Logarithmic equations
     1. log of both sides theorem
     2. four types
         a. the unknown is the logarithm
         b. the unknown is the base
         c. the logarithm of an unknown is equal to a number
         d. the logarithm of an unknown is equal to the logarithm of a number
C. Laws of logarithms
     1. additive law
     2. subtractive law
     3. multiplicative law   

10.2 Essential Ideas

Fundamental properties of logarithms (Grant's tomb properties):
            log_bb^x = x
            b^xlogb^x = x

A logarithmic equation is an equation for which there is a logarithm on one or both sides.  The key to solving logarithmic equations is the log of both sides theorem:  If A, B, and b are positive real numbers (with b not equal to 1), then
                                     log_bA = log_bB is equivalent to A = B.

Laws of Logarithms
If A, B, and b are positive numbers, p is any real numbers and b is not equal to 1:
First law (Addition):  log_b(AB) = log_bA + log_bB
Second law (Subtractive):  log_b(A/B) = log_bA - log_bB
Third law (Multiplicative):  log_bA^p = p log_bA