CLASS 11th COMMERCE (APPLIED MATHS ) L-3 INDICES & LOGARITHM FULL CHAPTER EXPLANATION By RAHUL SIR скачать в хорошем качестве

CLASS 11th COMMERCE (APPLIED MATHS ) L-3 INDICES & LOGARITHM FULL CHAPTER EXPLANATION By RAHUL SIR

CLASS 11th COMMERCE (APPLIED MATHS ) L-3 INDICES & LOGARITHM FULL CHAPTER EXPLANATION By RAHUL SIR Fundamental Laws of Indices If a, b are real numbers and m, n are rational numbers, the following laws apply: • Product Law: a^m \cdot a^n = a^{m+n}  • Quotient Law: \frac{a^m}{a^n} = a^{m-n}  • Power Law: (a^m)^n = a^{mn}  • Zero Index: a^0 = 1 (where a
eq 0) • Negative Index: a^{-n} = \frac{1}{a^n} • Fractional Index: a^{1/n} = \sqrt[n]{a} 2. Logarithms A logarithm is the power to which a base must be raised to yield a given number. It is the bridge between addition and multiplication.  Definition: If a^x = n, then \log_a n = x.  Types of Logarithms 1. Common Logarithm: Uses Base 10 (written as \log x).  2. Natural Logarithm: Uses Base e (\approx 2.718, written as \ln x).  Basic Laws of Logarithms These laws allow you to break down complex multiplication and division into simpler addition and subtraction:  • Product Rule: \log_a(m \cdot n) = \log_a m + \log_a n  • Quotient Rule: \log_a(\frac{m}{n}) = \log_a m - \log_a n  • Power Rule: \log_a(m^k) = k \cdot \log_a m  • Change of Base: \log_a b = \frac{\log_c b}{\log_c a}  • Unity & Zero: \log_a a = 1 and \log_a 1 = 0. Please subscribe 🙏❤️