Section 4.5: Logarithmic Functions Essential Ideas For positive b and A, b not equal to 1,            x = logbA     means      b x = A x is the called the logarithm and A is called the argument. Exponential Property of Equality For positive real numbers b (b not equal to 1)            b x = b y    if and only if     x = y Logarithmic Notations A common logarithm is base 10: log x means log10x A natural logarithm is base e :      ln x means logex Change of Base Theorem                            logax = logbx / logbA The function f defined for positive real numbers by                            f (x) = logbx where b > 0, b not equal to 1, is called the logarithmic function with base b. See the directory of curves for the graph of the logarithmic function Properties of Logarithms (Grant's Tomb Properties)              logbbx = x   The exponent on a base b which is b x is x. Duh.. .              b logbx = x   logbx is the exponent of a base b which gives x.                                  Double duh.... this is the definition of exponent.                                  See why these are called Grant's Tomb properties? The exponential and logarithmic functions with base b are inverse functions of one another. < Back to Section 5