Higher Algebra Hall & Knight Exponential & Logarithmic Series (Chapter 17) Solutions

Hall and Knight Higher Algebra Solutions Chapter 17 ‘Exponential and Logarithmic Series’ are created by subject matter experts at Instasolv to help you understand these concepts for engineering entrance exams like JEE Mains and JEE Advanced. These solutions discuss topics like natural logarithms, logarithmic series and some formulae adopted for calculating common logarithms. The topics are covered in a detailed manner that will help you to understand new tips and tricks. Also, the solutions contain many solved examples that will help you in assembling all the concepts dealt in the chapter. 

Higher Algebra by Hall and Knight Chapter 17 contains 1 exercise with 24 questions The questions designed by Hall and Knight are according to the latest competitive exams pattern and will help you form a solid foundation of exponential and logarithmic series. These solutions will help you find the Napierian Log of a series, numerical values of common logarithms, the general terms of logarithmic series and the sum of a logarithmic series. All the solutions include step by step procedures of solving problems to help you understand the concepts better. 

From providing 100% accurate and easy to understand solutions for Elementary Algebra and Higher Algebra by Hall and Knight, we make the course content easy for you. We ensure to follow the latest study material for JEE and other common competitive exams so that you can prepare for them easily by referring to our solutions. Refer to our solutions for free at any time and make your study time fruitful. 

Important Topics for Hall and Knight Higher Algebra Solutions Chapter 17: Exponential and Logarithmic Series

What are Natural Logarithms?

The logarithm to the base of any mathematical constant e is known as the natural logarithm of number. Here ‘e’ is an irrational and transcendental number. The value of e is approximately equal to 2.718.

To take an example of a natural logarithm write as one logarithm ⅓ ln(x-1) – ½ ln(x +1) + 2ln x. Start solving the problem by converting it like ln(x-1)1/3 – ln(x+1)1/2 + lnx2. This way the entire problem can be solved easily using the given formula of natural logarithms.

The natural, as well as common logarithm, can easily be found all around algebra as well as calculus. The common logarithm consists of base 10 and on a calculator, it is shown as log(x). On the other hand, the natural logarithm has the base e which is a famous irrational number and on the calculator, it is shown as ln(x).

What is a logarithmic series?

The calculation of logarithmic numbers to the base e are known as natural logarithms or Napierian logarithms. On the other hand, numbers calculated to the base 10 are known as common logarithms.

We are required to convert Napierian Logarithms into common logarithms using the formula ( log10 n = loge/loge10). Hence,  In order to find the logarithms of any number to the base 10, you can multiply the logarithms of the number to the base e by 0.43429448.

Exercise Discussion of  Higher Algebra by Hall and Knight Chapter 17: Exponential and Logarithmic Series

  • Chapter 17 ‘Exponential and Logarithmic Series’ of Higher Algebra By H.S. Hall and S.R. Knight consists of a single exercise with a total number of 24 questions. 
  • The questions cover two topics of this chapter that is logarithmic series and natural logarithm. 
  • These questions are unsolved which might be quite challenging for you but will help you prepare for upcoming exams.
  • In the exercise, you will have to answer the questions using the formulas of logarithm given in the chapter,
  • Once you start solving the exercise you will experience questions like: if x < 1 then find the sum of the given series, expand the given equation in a series of ascending powers of x, and many other equations will be given that you are required to solve.

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  • Our subject matter experts are devoted to helping you by offering you solutions that are easy to understand and are elaborated in a step by step manner. 
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