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Change of a Base Formula For all positive numbers a, b, and n, where a does not equal 1 and b does not equal 1. Common Logarithm Logarithms that use 10 as the base. Exponential Decay Exponential decay occurs when a quantity decreases exponentially over time. Exponential Equation An equation in which the variables occur as exponents. Exponential Function A function of the form y=ab^x, where a does not equal 0, and b does not equal 1. Exponential Growth Exponential growth occurs when a quantity increases exponentially over time. Exponential Inequality An inequality that does not satisfy the original equation. Logarithm In the function x=b^y, y is called the logarithm, base b, of x. Usually written as y=log^bx and is read "y equals log base b of x." Logarithmic Equation An equation that contains one or more logarithms. Logarithmic Function The function y=log^bx, where b>0 and b does not equal 1, which is the inverse of the exponential function y=bx. Logarithmic Inequality An inequality that contains one or more logarithms. Natural Base, e An irrational number approximately equal to 2.71828... . Natural Base Exponential Function An exponential function with the base e, y=e^x. Natural Logarithm Logarithms with base e, written in x. Natural Logarithmic Function y=In x, the inverse of the natural base exponential function y=e^x. Rate of Decay The percent decrease r in the equation y=a(1-r)^t. Rate of Growth The percent increase r in the equation y=a(1+r)^t.