# S.L. Loney Logarithms Solutions (Chapter 10)

SI Loney Plane Trigonometry Solutions Chapter 10: Logarithms is a well-built textbook solution designed for those who wish to improve their practical understanding of Logarithms. Students who choose to attend a multivariable calculus course or compete in competitive tests such as JEE must have this book because it has a range of well-resolved and unanswered questions for a detailed examination.

If we discuss the numbers and kinds of questions in Chapter 10: Logarithms of SI Loney Trigonometry Solutions Book provides, a total of 13 questions that are divided into the problem- based (numerical) and theoretical questions alongside 13 solved examples. Here in this chapter, you will get to know some of the common systems within logarithms, its characteristics, and Mantissa, number determination by inspection at the decimal fraction. As you proceed with this chapter you will get to know that Mantissa of the logarithm of all numbers, consisting of the same digits, is the same. You will learn how to use a table of a logarithm to solve different problems in exams.

We provide comprehensive solutions to SL Loney Trigonometry developed by our experts and professionals, which are readily accessible online. This book deals with different principles of logarithms in a practical way, and our approaches will give you the edge that is so much required to crack those tough exams like JEE and NEET. You will learn lots of tactics and get ideas on how questions are solved.

## Important Topics for SI Loney Plane Trigonometry Solutions Chapter 10: Logarithms

- Logarithms are another way of thinking about exponents.
- In advanced mathematics, the logarithm is the inverse function of exponents. This implies that the logarithm of a specified number x is the exponent to which another defined total number, base b, must be applied in order to obtain the number x. In the simplest case, the logarithm counts the number of instances of a similar factor while the multiplication is repeated;
**For example:**even though 1000 = 10 × 10 × 10 = 10^{3}, the “logarithm base 10” of 1000 will be 3, or log_{10}(1000) = 3.

The logarithm of” x” to base” b” is denoted by log_{b} (x)

- For both the exponential functions and the logarithms, the base may be any number. There are, however, two bases that are used so commonly those mathematicians have different names for their logarithms, and complex mathematical and graphic calculators have keys especially for them. Those are the common and natural logarithms.
- Any logarithm with base 10 is a common logarithm. You should remember that our total number system is base 10; there are ten digits from 0-9, and their place value is calculated by groups of 10. You should recall a “common logarithm,” instead, as every logarithm whose base is our “common base” =10.
**Natural logarithms**are distinct from common logarithms. While the base of such a logarithm is 10, the base of the natural logarithm is the unique number e. While this tends to be a variable, it reflects a defined arbitrary number roughly equal to 2,718281828459.**Properties of Logarithms:**

- Properties 3 and 4 lead to a good relationship between the logarithm and exponential function. Let’s measure the following feature compositions first for f(x)=bxf(x)=bx and g(x)=logbxg(x)=logbx.

- Do Recall the Inverse Functions segment that this implies that the exponential and logarithmic functions are inversely related.
- The 1
_{st}and 2_{nd }properties mentioned here can be a little misleading because at first as on one side we have a value or a quotient within the logarithm and on the other side, we have a sum or a huge discrepancy of two logarithms. You need to be extra careful while applying these properties to make sure you use them correctly in numerical. **Point to be noted:**There are no rules on how to break down the logarithm of the sum or the difference between two terms.

**Characteristics and mantissa:**

When the logarithm of any significant number is partly integral and partly fractional, the integral component of the logarithm is called mantissa, and the decimal section is called the mantissa. Negative characteristics:

Let us take,

Log 2 = .30103

Then,

Log ½ = log 1 – log2 = 0 -log 2 = – .30103

log ½ is negative.

**Description of Characteristic and Mantissa:**

The logarithm of a number is calculated by the examination and the mantissa by the logarithm table.

**In order to find the functional characteristics of the logarithm of a number greater than 1: **As we know, log 1 = 0 and log 10 = 1 are, therefore, the common logarithm of a number between 1 and 10 (i.e., the integral part of which mainly consists of only one digit) is in between 0 and 1. The function of a logarithm of a number greater than 1 is positive and is one less than the number of digits in the integral portion of the number.

**Finding characteristic of the logarithm of a number lying in between 0 and 1:** As we know the log.1 = -1 and log 1 = 0, common logarithm of a number between.1 and 1 are between-1 and 0.The definition of the logarithm of a positive integer less than 1 is negative and is numerically larger than the sum of zeros in between the decimal sign and the first significant and meaningful integer**.**

**Finding mantissa**[using log-table]:

After deciding the characteristics of the logarithm of a positive number through observation, the mantissa of the logarithm is calculated by the logarithm table. All four-figure and five-figure tables are seen at the conclusion of the book. A four-figure table provides the right mantissa meaning to four decimal points.

- In the same way, a five-figure or a nine-figure log-table provides the right mantissa meaning to five or nine decimal points.
- In advanced mathematics, the logarithm table is used to calculate the value of the logarithm equation. The easiest way to find the actual value of the logarithmic function is to use the log table.
- An antilog, also known as “Anti-Logarithms,” of a series, is the opposite technique of locating the same series of logarithms. Remember, if x is the logarithm of the number y with base b, then we can assume that y is the antilog of x to base b. This is described by

log_{b} y = x Then, y = antilog x

- The logarithm and antilog have a basis of 2,7183. When the logarithm and antilogarithm have a base of 10, it can be translated to natural logarithm and antilog by multiplying the number by 2,303.
- How to Use a Log Table?
**Step 1**: Every log table may only be used for a certain base. Log base 10 is the most common form of logarithm table used.**Step 2:**identification of characteristics and mantissa part of the given number.**Step 3**: using a common log table.**Step 4:**Using a logarithm table has a mean difference.**Step 6**: Identify the characteristic part.**Step 7**: the last step is the combination of the characteristic part and the mantissa part both.

### Discussion of Exercises of SI Loney Plane Trigonometry Solutions Chapter 10: Logarithms

This chapter is divided into two sets of questionnaires. They are exercise-based questions and additional solved examples.

- The first set is exercise-based questions that have a total of 13 questions that are further divided into two parts: problem-based and theoretical questions.
**Problem-based questions**will help you to understand the basic techniques of using a log table to solve complex mathematical calculations in the easiest possible way.**Theoretical questions**mainly help you to learn the basic characteristics of a logarithm, their properties and types. You will get to know about the characteristics and mantissa.

## Why Use SI Loney Plane Trigonometry Solutions Chapter 10: Logarithms by instasolv?

- We offer complete answers to all difficult questions in SI Loney Plane Solutions Chapter 10: Logarithms by instasolv, which is of great benefit to JEE and NEET aspirants to efficiently solve difficult problems and plan accordingly their time throughout their final examinations.
- InstaSolv is designed in a manner that helps you to thoroughly grasp every aspect of the chapter so that you don’t have any uncertainty in your mind when learning about it.