Logarithmic Identity: logb1 = 0, Logarithmic of Base: logbb = 1, Logarithm of a Product: logb(xy) = logbx + logby, Logarithm of a Quotient: logb(x/y) = logbx - logby, Logarithm of a Power: logb(x)n = nlogbx, Change of Base Formula: logbx = logcx / logcb, Logarithm of the Reciprocal: logb(1/x) = -logbx, Logarithm of Exponentiation: logbbx = x These rules are essential for simplifying logarithmic expressions, solving logarithmic equations, and performing calculations involving logarithmic functions.