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This is a standard limit that defines the derivative of the function f(x) = a^x at x = 0.The definition of the derivative f'(c) is limx→c (f(x) - f(c)) / (x - c).Here, f(x) = a^x and c = 0.So, limx→0 (a^x - a^0) / (x - 0) = f'(0).We know that the derivative d/dx (a^x) = a^x ln a (or a^x log_e a).Therefore, f'(0) = a^0 ln a = 1 * ln a = ln a.In higher mathematics, 'log a' often refers to the natural logarithm (ln a) when the base is not specified.