Calculate logarithm and exponential using simple calculator

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Is there a formula/way how to calculate logarithm precisely like log(3.587) or calculate 5^0.358 just using simple calculator.. I mean calculate precisely like scientific calculator not in estimation result.

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By adding, subtracting, multiplying and dividing you can calculate exponentials and logarithms with arbitrarily high precision using their respective Taylor series.

Unfortunately, you cannot, in general, get a precise decimal expansion of those numbers, as you will very often encounter irrationals!