I understand the properties of logarithms. However I am curious if a calculator uses complex power series, slide rule program, Taylor series, or a form of an algorithm to solve for log"base"n(x).
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1One way or the other, read up on CORDIC (https://en.wikipedia.org/wiki/CORDIC). It's amazing how all calculator functions can use the same algorithm: exp/log, sqrt, trig/hyperbolic trig, its inverse functions,... all just different parameters, same algorithm. Ingenious, really. – orion Feb 19 '16 at 07:58