Réponse :
Explications étape par étape
Bonjour
e^x * e^2 = e^(-3)
e^x = e^(-3)/e^2
Ln e^x = ln(e^(-3)/e^2)
x = ln(e^(-3)) - ln e^2
x = -3 - 2
x = -5
Ln x + ln 2 = -3
Ln (2x) = -3
e(Ln (2x)) = e^(-3)
2x = e^(-3)
x = e^(-3)/2
x ~ 0,025
Ln x + ln (x - 1) = ln 6
Ln[x(x - 1)] = ln 6
e(ln[x(x - 1)]) = e(ln 6)
x(x - 1) = 6
x^2 - x - 6 = 0
[tex]\Delta = (-1)^2 - 4 \times 1 \times (-6) = 1 + 24 = 25[/tex]
[tex]\sqrt\Delta = 5[/tex]
X1 = (1 - 5)/2 = -4/2 = -2
X2 = (1 + 5)/2 = 6/2 = 3
[tex]3e^{0,5x} + 4 \ge 16[/tex]
[tex]3e^{0,5x} \ge 16 - 4[/tex]
[tex]3e^{0,5x} \ge 12[/tex]
[tex]e^{0,5x} \ge \dfrac{12}{3}[/tex]
[tex]e^{0,5x} \ge 4[/tex]
[tex]ln e^{0,5x} \ge ln 4[/tex]
[tex]0,5x \ge ln 4[/tex]
[tex]x \ge (ln 4)/0,5[/tex]
[tex]x \ge 2,773[/tex]
[tex]x \in [2,773 ; +\infty[[/tex]
Ln(x + 1) < 2
e[ln (x + 1)] < e^2
x + 1 < e^2
x < e^2 - 1
x < 6,389
[tex]x \in ]-\infty ; 6,389 [[/tex]
