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logarithms_def_eng, <math xmlns="http://www.w3.org/1998/Math/MathML"> <mrow> <mtext> differences: </mtext> <mmultiscripts> <mtext> log </mtext> <mtext> b </mtext> <none/> </mmultiscripts> <mtext> p - </mtext> <mrow> <mmultiscripts> <mtext> log </mtext> <mtext> b </mtext> <none/> </mmultiscripts> <mtext> q = </mtext> <mrow> <mmultiscripts> <mtext> log </mtext> <mtext> b </mtext> <none/> </mmultiscripts> <mtext> ( </mtext> <mrow> <mtext> </mtext> <mfrac> <mtext> p </mtext> <mtext> q </mtext> </mfrac> </mrow> <mtext> ) </mtext> </mrow> </mrow> </mrow> </math> yield the result (n) through antilogarithm, <math xmlns="http://www.w3.org/1998/Math/MathML"> <mrow> <mtext> products: q· </mtext> <mmultiscripts> <mtext> log </mtext> <mtext> b </mtext> <none/> </mmultiscripts> <mtext> p </mtext> <mrow> <mtext> = </mtext> <mrow> <mmultiscripts> <mtext> log </mtext> <mtext> b </mtext> <none/> </mmultiscripts> <mrow> <mrow> <mtext> </mtext> <mmultiscripts> <mtext> p </mtext> <none/> <mtext> q </mtext> </mmultiscripts> </mrow> </mrow> </mrow> </mrow> </mrow> </math> yield the result (n) through antilogarithm, rational exponent x can be generalized to a Continuous function of R, antilogarithm obtained thanks to Logarithmic tables, antilogarithm obtained thanks to calculator, <math xmlns="http://www.w3.org/1998/Math/MathML"> <mtext> Logarithm of n∈ </mtext> <mmultiscripts> <mtext> R </mtext> <none/> <mtext> + </mtext> </mmultiscripts> </math> is a rational exponent x, <math xmlns="http://www.w3.org/1998/Math/MathML"> <mtext> Logarithm of n∈ </mtext> <mmultiscripts> <mtext> R </mtext> <none/> <mtext> + </mtext> </mmultiscripts> </math> facilitates <math xmlns="http://www.w3.org/1998/Math/MathML"> <mrow> <mtext> raising to power,
as far as n = </mtext> <mmultiscripts> <mtext> p </mtext> <none/> <mtext> q </mtext> </mmultiscripts> <mtext> , </mtext> </mrow> </math>, <math xmlns="http://www.w3.org/1998/Math/MathML"> <mrow> <mtext> raising to power,
as far as n = </mtext> <mmultiscripts> <mtext> p </mtext> <none/> <mtext> q </mtext> </mmultiscripts> <mtext> , </mtext> </mrow> </math> are changed in <math xmlns="http://www.w3.org/1998/Math/MathML"> <mrow> <mtext> products: q· </mtext> <mmultiscripts> <mtext> log </mtext> <mtext> b </mtext> <none/> </mmultiscripts> <mtext> p </mtext> <mrow> <mtext> = </mtext> <mrow> <mmultiscripts> <mtext> log </mtext> <mtext> b </mtext> <none/> </mmultiscripts> <mrow> <mrow> <mtext> </mtext> <mmultiscripts> <mtext> p </mtext> <none/> <mtext> q </mtext> </mmultiscripts> </mrow> </mrow> </mrow> </mrow> </mrow> </math>, <math xmlns="http://www.w3.org/1998/Math/MathML"> <mrow> <mtext> sums: </mtext> <mmultiscripts> <mtext> log </mtext> <mtext> b </mtext> <none/> </mmultiscripts> <mtext> p + </mtext> <mrow> <mmultiscripts> <mtext> log </mtext> <mtext> b </mtext> <none/> </mmultiscripts> <mtext> q = </mtext> <mrow> <mmultiscripts> <mtext> log </mtext> <mtext> b </mtext> <none/> </mmultiscripts> <mtext> (p·q) </mtext> </mrow> </mrow> </mrow> </math> yield the result (n) through antilogarithm, <math xmlns="http://www.w3.org/1998/Math/MathML"> <mtext> Logarithm of n∈ </mtext> <mmultiscripts> <mtext> R </mtext> <none/> <mtext> + </mtext> </mmultiscripts> </math> facilitates multiplications, when n = p·q,