Скачать с ютуб Basic properties of logarithm ||step by step problems solved|| в хорошем качестве

Basic properties of logarithm ||step by step problems solved||

#algebra Logarithms simplify calculations involving large numbers by expressing them in terms of powers. They are widely used in mathematics, science, and engineering to handle exponential relationships. The fundamental properties of logarithms help in simplifying expressions and solving logarithmic equations. Basic Properties of Logarithms 1. Product Rule When two numbers are multiplied inside a logarithm, their logarithms can be added: The logarithm of a product is equal to the sum of the logarithms of the individual numbers. Example: The logarithm of 1000 multiplied by 100 is the same as the logarithm of 1000 plus the logarithm of 100. 2. Quotient Rule When one number is divided by another inside a logarithm, their logarithms can be subtracted: The logarithm of a fraction is equal to the logarithm of the numerator minus the logarithm of the denominator. Example: The logarithm of 1000 divided by 10 is the same as the logarithm of 1000 minus the logarithm of 10. 3. Power Rule When a number inside a logarithm is raised to a power, the exponent can be moved in front as a multiplier: The logarithm of a number with an exponent is equal to the exponent multiplied by the logarithm of the base number. Example: The logarithm of 100 squared is twice the logarithm of 100. 4. Change of Base Rule A logarithm with one base can be rewritten using a different base: The logarithm of a number with one base can be expressed as a fraction of two logarithms using another base. Example: A logarithm with base 2 can be rewritten using base 10 by dividing the logarithm of the number (in base 10) by the logarithm of 2 (in base 10). 5. Logarithm of 1 The logarithm of 1 in any base is always equal to zero: Since any number raised to the power of zero equals 1, the logarithm of 1 is always 0. Example: The logarithm of 1 in base 5 is 0. 6. Logarithm of the Base The logarithm of a base number in that same base is always equal to 1: Since any number raised to the power of 1 is itself, the logarithm of a base in that same base is always 1. Example: The logarithm of 10 in base 10 is 1. Applications of Logarithms These properties are used in various fields, including: Mathematics – Simplifying calculations and solving equations. Physics – Measuring sound levels and earthquake magnitudes. Computer Science – Analyzing algorithm efficiency. Finance – Calculating interest rates and investment growth. Understanding these basic properties is essential for working with logarithms effectively. For more detailed explanations and step-by-step tutorials, subscribe to Inorganic Tutor!#algebra