Fct Logarithme

Question 1

What is the base of the natural logarithm?

Answer 1

The base of the natural logarithm is e, approximately equal to 2.71828.

Question 2

True or False: The natural logarithm of 1 is 0.

Answer 2

True.

Question 3

Fill in the blank: The natural logarithm is denoted as _____.

Answer 3

ln

Question 4

What is the derivative of the natural logarithm function, ln(x)?

Answer 4

The derivative of ln(x) is 1/x.

Question 5

Which of the following is true about ln(ab)? A) ln(a) + ln(b) B) ln(a) - ln(b) C) ln(a/b) D) ln(a^b)

Answer 5

A) ln(a) + ln(b)

Question 6

What is the integral of the natural logarithm function, ln(x)?

Answer 6

The integral of ln(x) is x ln(x) - x + C, where C is the constant of integration.

Question 7

True or False: The natural logarithm function is defined for negative numbers.

Answer 7

False.

Question 8

What is the value of ln(e)?

Answer 8

The value of ln(e) is 1.

Question 9

If y = ln(x), what is the relationship between x and y when x = e^3?

Answer 9

If y = ln(x), then when x = e^3, y = 3.

Question 10

Which property of logarithms states that ln(a^b) = b * ln(a)?

Answer 10

The power rule of logarithms.