La fonction Logarithme et la fonction exponentiel

Résolvez l'équation logarithmique suivante : log(x) = 3

• 2

• 10

• 1000

• 5

Answer explanation

To solve the equation log(x) = 3, we use the property that log base 10 of 1000 equals 3. Therefore, the correct answer is 1000.

Utilisez les propriétés des logarithmes pour simplifier log(2x) + log(3)

• log(6x)

• log(5x)

• log(2x + 3)

• log(2) + log(3)

Answer explanation

By using the property log(a) + log(b) = log(ab), the expression log(2x) + log(3) simplifies to log(6x), which is the correct choice.

Calculez la valeur de l'expression exponentielle : e^5

• e^5 = 148.4131591

• e^5 = 200

• e^5 = 100

• e^5 = 25

Answer explanation

The correct value of the exponential expression e^5 is 148.4131591.

Appliquez la règle de dérivation pour trouver la dérivée de f(x) = e^x

• f'(x) = e^x

• f'(x) = x^e

• f'(x) = e^(x-1)

• f'(x) = 2e^x

Answer explanation

The correct answer is f'(x) = e^x because the derivative of e^x is e^x according to the rule of differentiation for exponential functions.

Quelle est la croissance exponentielle de la fonction f(x) = 2^x ?

• Une croissance exponentielle

• Une croissance linéaire

• Une croissance logarithmique

• Une croissance quadratique

Answer explanation

The function f(x) = 2^x exhibits exponential growth, as the variable x is in the exponent, leading to an exponential increase in the function's value.

Résolvez l'équation logarithmique suivante : log(2x) = log(4) + log(3)

• x = 2

• x = 10

• x = 12

• x = 6

Answer explanation

By using the property log(a) + log(b) = log(ab), the equation simplifies to log(2x) = log(12). Therefore, x = 6.

Utilisez les propriétés des logarithmes pour simplifier log(x^3) - log(x)

• 3

• 3x

• x^2

• x^3 - x

Answer explanation

By using the properties of logarithms, we can simplify log(x^3) - log(x) to 3log(x) - log(x) = 2log(x) = log(x^2). Therefore, the correct answer is x^2.

Calculez la valeur de l'expression exponentielle : e^(-2)

• e^-2

• e^2

• -1/e^2

• 1/e^2

Answer explanation

The correct answer is 1/e^2 because e^(-2) is equivalent to 1/(e^2), which is approximately 0.135.

Appliquez la règle de dérivation pour trouver la dérivée de f(x) = ln(x)

• x^2

• 2x

• 1/x

• cos(x)

Answer explanation

The derivative of ln(x) is 1/x according to the rule of differentiation for natural logarithm functions.

Quelle est la croissance exponentielle de la fonction f(x) = 3^x ?

• 9

• 3

• 2

• 5

Answer explanation

The exponential growth of the function f(x) = 3^x is 3, as the base of the exponential function is 3.