Section 10.2: Logarithmic Equations 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 bx.            b. logbx 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):             logbbx = x             bxlogbx = 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                                      logbA = logbB 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):  logb(AB) = logbA + logbB Second law (Subtractive):  logb(A/B) = logbA - logbB Third law (Multiplicative):  logbAp = p logbA