La forma de esta función es f(x) = loga(x) donde "a" es constante (un número) y se denomina la base del logaritmo[br][br]Las características generales de las funciones logarítmicas son:[br][br]1) El dominio de una función logarítmica son los números reales positivos: Dom(f) = (0. + ∞) .[br]2) Su recorrido es R:Im(f) = R .[br]3) Son funciones continuas.[br]4) Como loga1 = 0 , la función siempre pasa por el punto (1, 0) .[br] 5) Como logaa = 1 , la función siempre pasa por el punto (a, 1) .[br][br] Si a > 1 la función es creciente.[br]Si 0 < a < 1 la función es decreciente.[br][br]Son convexas si a > 1 .[br]Son concavas si 0 < a < 1 .[br][br]El eje Y es una asíntota vertical.[br][br]Si a > 1 :[br][br]Cuando x → 0 + , entonces log a x → - ∞[br][br]Si 0 < a < 1 :[br][br]Cuando x → 0 + , entonces log a x → + ∞[br][br]Su dominio...[br][br]El dominio de las funciones logarítmicas es (0, + ∞) .[br]Dom(f) = Dom(g) = (0, + ∞) .[br][br] Puntos de corte:[br][br]f(1) = log21 = 0 , el punto de corte con el eje X es (1, 0).[br]g(1) = log1/21 = 0 , el punto de corte con el eje X es (1, 0).[br]La funciones f(x) y g(x) no cortan al eje Y.[br][br]Crecimiento y decrecimiento:[br][br]La función f(x) es creciente ya que a > 1 .[br]La función g(x) es decreciente ya que 0 < a < 1 .[br][br]Asíntotas:[br]Las funciones f(x) y g(x) tienen una asintota en el eje Y.[br][br]Ejemplo de gráfica:[br][br][img]data:image/jpeg;base64,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