Question

Am o intrebare: cum se descompuneau logaritmii?

De exemplu: eu stiu ca log₂ 5= a si log₂ 3= b
Sa se calculeze log₈ 75.

Answer 1

$log_{b}a= \frac{ log_{A} a}{ log_{A}b } \\ log_{8}75= \frac{ log_{2} 75}{ log_{2}8 }= \frac{ log_{2} (3* 5^{2}) }{ 3 } = \frac{ log_{2} 3+2 log_{2}5 }{ 3 } = \frac{ b+2a}{ 3 }$