Forum de Mathématiques: Maths-Forum

{logx(10) + logy(10) = 7/3 (1) {log(xy)=7/2 (2) Réponse : où (2) on a produit xy = 10^(7/2) De (1) on a 1/logx + 1/logy = 7/3 =>( logx + log y)/ (logx*logy) = 7/2 => logxy / (logx*logy) = 7/2 => 1/(3logx*logy) = 1/2 => logx*logy = 2/3 (3) Remplace x= [10^(7/2)]/y en (3 ) on a : log[(10^(7/2))/y] * l...

1) x²f(x) = 5lnx => (x²f(x))' = 5/x 2xf(x) + x²f'(x) = 5/x f'(x) = (5/x- 2xf(x))/x² = [5(1-2lnx)]/x^3 2) f'(x) = 0 => x= e^(1/2) calcul f(2); f(e^(1/2)); f(10) Tracer la table de variation 3) appussant sur la table de variation pour indiquer il y a unique une solution dans ce cas ! :zen: