see also:

• a brief summary of mathematical principles and tools
• History of Mathematics
• mensuration - how to measure area, volume, etc of various shapes
• Algebra
• Calculus
• Circular functions
• Coordinate geometry, parabolae, etc
• Finance equations
• Probability theory

• 1614, John Napier, publicly propounded the method of logarithms
• in the 18thC, Leonhard Euler gave the current definition of the constant e, the base of the natural logarithm, still known as Euler's number and introduced the use of the exponential function and logarithms in analytic proofs

• loga(x) + loga(y) = loga(xy);
• log(1) = 0;
• loga(x) - loga(y) = loga(x/y);
• ploga(x) = loga(x^p);
• logb(x)= loga(x)/loga(b);
• complex numbers in logs:
  • log(cosb + isinb) = ib

• a^m * a^n = a^(m+n);
• a^m/a^n = a^(m-n);
• (a^m)^n = a^(mn);
• (ab)^n = a^n * b^n;
• a^(-n) = 1/a^n;
• a^0 = 1;
• a^(1/q), where q is positive integer, a>0,
  • then, = positive qth root of a;
• x^y = Exp(y * Ln(x)); where exp(z) is e to power of z.

• sinhx = 0.5(e^x - e^(-x));
• coshx = 0.5(e^x + e^(-x));
• tanhx = (e^x - e^(-x))/(e^x + e^(-x));