Exercises on natural logarithms are essential for high school seniors in the United States education system. They cover a variety of concepts and calculation techniques that are at the core of the mathematics curriculum, allowing students to practice independently with hints, course reminders, and methodological advice.
For example, exercises often ask students to express a natural logarithm in terms of another. A typical exercise might involve simplifying a natural logarithm containing a power. These types of exercises help students understand and manipulate the properties of logarithms to simplify complex expressions.
Other exercises focus on simplifying natural logarithms containing quotients. For example, expressing one natural logarithm in terms of another teaches students how to break down and simplify logarithmic expressions that involve fractions.
Some exercises also require students to simplify the product of a fraction and a natural logarithm containing a quotient. For example, expressing the product of a fraction and a natural logarithm in terms of another helps them practice distributing and simplifying logarithms in multiplied expressions.
Students also learn to simplify the natural logarithm of a square root. For example, expressing the natural logarithm of a square root in terms of another helps them master transforming logarithms involving roots.
In addition to simplifying logarithmic expressions, some exercises ask students to calculate antiderivatives and derivatives involving natural logarithms. For example, calculating an antiderivative of a rational function of the first degree or the second degree over the set of positive real numbers helps reinforce their understanding of integrals and derivatives in relation to natural logarithms.
These exercises are designed to reinforce students' understanding and prepare them for exams by providing thorough and varied practice in methods of calculation related to natural logarithms.
8 exercisesExercise example N°1709 :
Express ln(25) as a function of ln(5) .
neperian logarithm functions 12th Grade
The purpose of this corrected exercise is to simplify a neperian logarithm containing a power.
Exercise example N°1710 :
Express `ln(1/27)` as a function of ln(3)
neperian logarithm functions 12th Grade
The goal of this corrected exercise is to simplify a neperian logarithm containing a quotient.
Exercise example N°1711 :
Express `-3/8*ln(1/(27))` as a function of ln(3)
neperian logarithm functions 12th Grade
The goal of this corrected exercise is to simplify the product of a fraction and a neperian logarithm containing a quotient.
Exercise example N°1712 :
Express `-5/8*ln(sqrt(2))` as a function of ln(2)
neperian logarithm functions 12th Grade
The aim of this corrected exercise is to simplify the neperian logarithm of a square root.
Exercise example N°1713 :
Compute an antiderivative of the function `f(x)=7/(9+7*x)` on `RR^+` .
neperian logarithm antiderivatives functions 12th Grade antiderivative
The aim of this corrected exercise is to use the neperian logarithm to calculate one of the primitives of a rational fraction of the first degree.
Exercise example N°1714 :
Compute an antiderivative of the function `f(x)=(8*x)/(1+4*x^2)` on `RR^+` .
neperian logarithm antiderivatives functions 12th Grade antiderivative
The goal of this corrected exercise is to use the neperian logarithm for antiderivative calculation of a rational fraction of degree 2.
Exercise example N°1715 :
Calculate the derivative of the function `ln(x)^5`.
neperian logarithm derivatives of functions functions 12th Grade derivative
The goal of this corrected exercise is to use the neperian logarithm to calculate the derivative.
Exercise example N°1716 :
Calculate the derivative of the function `ln(9+9*x^2)`.
neperian logarithm derivatives of functions functions 12th Grade derivative
The goal of this corrected exercise is to use the neperian logarithm to calculate the derivative.