Logarithms are indispensable tools in mathematics, simplifying complex calculations and making exponential growth and decay problems manageable. The laws of logarithms provide rules to work efficiently with logarithmic expressions, while their applications span diverse fields such as science, engineering, and finance. This article delves into the fundamental laws of logarithms and their real-world uses, helping…
1. Find the characteristic of the following numbers (i) \(5287\) \[\text{Characteristic }= 3\] (ii) \(59.28\) \[\text{Characteristic }= 1\] (iii) \( 0.0567\) \[\text{Characteristic }=\overline{2}\] (iv) \(234.7\) \[\text{Characteristic }= 2\] (v) \(0.000049\) \[\text{Characteristic }=\overline{5}\] (vi) \(145000\) \[\text{Characteristic }= 5\] 2 Find the logarithm of the following numbers (i) \(43\) \[\text{Characteristic }= 1\] \[\text{Mantissa }= 6335\] \[\log(43) =…
Logarithms are powerful tools in mathematics, widely used in science, engineering, and everyday problem-solving. Understanding their key types, such as common and natural logarithms, along with related concepts like mantissa, characteristic, and antilogarithms, is essential for mastering exponential and logarithmic equations. This article provides a detailed yet simple explanation of these terms, complete with formulas…
1. Express each of the following in logarithmic form: (i) \( 10^3 = 1000 \) \[\log_{10} 1000 = 3\] (ii) \( 2^8 = 256 \) \[\log_{2} 256 = 8\] (iii) \( 3^{-3} = \frac{1}{27} \) \[\log_{3} \frac{1}{27} = -3\] (iv) \( 20^2 = 400 \) \[\log_{20} 400 = 2\] (v) \( 16^{-\frac{1}{4}} = \frac{1}{2} \)…
Logarithms are one of the most useful mathematical concepts, simplifying complex calculations and enabling us to solve problems involving exponential growth and decay. From scientific research to everyday applications like pH calculations or measuring sound intensity, logarithms are a fundamental tool. This article provides a clear definition of logarithms, their formulas, and examples to help…
Express the following numbers in scientific notation: (i) \( 2000000 \) \[2000000 = 2.0 \times 10^6\] (ii) \( 48900 \) \[48900 = 4.89 \times 10^4\] (iii) \( 0.0042 \) \[0.0042 = 4.2 \times 10^{-3}\] (iv) \( 0.0000009 \) \[0.0000009 = 9.0 \times 10^{-7}\] (v) \( 73 \times 10^3 \) \[73 \times 10^3 = 7.3 \times…
Logarithms and scientific notation are essential mathematical tools for simplifying complex calculations. Whether you’re dealing with extremely large or small numbers, these concepts allow for easy representation and manipulation. This article explores logarithms, scientific notation, and the processes for converting numbers between ordinary and scientific notation. By mastering these techniques, you can enhance your problem-solving…
Unlock the complete solution to Review Exercise 1 from the new 9th Class Math syllabus by Punjab Curriculum and Textbook Board (PCTB), Lahore. This step-by-step guide is designed to help students master the latest concepts with ease and confidence. Questions with Correct Options and Explanations: 1. \(\sqrt{7}\) is: (a) integer (b) rational number (c) irrational…
Explore the complete solution of Exercise 1.3 from the new Math 9th syllabus designed by the Punjab Curriculum and Textbook Board (PCTB), Lahore. This detailed guide simplifies the latest 9th class math concepts to help students excel in their studies 1. The sum of three consecutive integers is forty-two. Find the three integers. Let the…
Real numbers play a vital role in our daily activities, from managing finances to measuring temperatures. Their versatility enables us to solve real-world problems effectively. This article delves into the applications of real numbers in everyday life, focusing on temperature conversion and calculating profit and loss. By understanding these concepts, we can make informed decisions…
