Exponentials and logarithms

• If f(x) = e^x, then f'(x) = e^x.
• If f(x) = e^kx, f'(x) = ke^kx.
• Exponential graphs of the form f(x) = a^x have a similar shape graph to the graphs of their gradient functions. When original and gradient function graphs are identical, a = e.
• log a (n) = x is equivalent to a^x =n.
• log a (x) + log a (y) = log a (x y).
• log a (x) - log a (y) = log a (x/y).
• log a (x^k) = k log a (x).
• log a (1/x) = - log a (x)
• log a (a) = 1.
• log a (1) = 0.
• The graph of y = ln x is a reflection of the graph y = e^x in the line y = x.
• e^ln x = x and ln(e) = 1.
• ln x = log e (x).