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Logarithm - Basics Video Lecture - CAT
FAQs on Logarithm - Basics Video Lecture - CAT
| 1. What is a logarithm? |  |
Ans. A logarithm is a mathematical function that represents the exponent to which a base number must be raised to obtain a given number. In other words, it is the inverse operation of exponentiation. For example, if we have the equation 10^x = 100, the logarithm function can be used to find that x is equal to 2.
| 2. How do logarithms work? | |
Ans. Logarithms work by converting exponential equations into simpler linear equations. The logarithm of a number to a given base is the exponent to which the base must be raised to obtain that number. For example, if we have the equation 2^x = 8, we can rewrite it as log base 2 of 8 equals x, which simplifies to x = 3.
| 3. What are the properties of logarithms? | |
Ans. Logarithms have several properties that make them useful in mathematical calculations. Some of the key properties include:
- The logarithm of a product is equal to the sum of the logarithms of the individual factors.
- The logarithm of a quotient is equal to the difference of the logarithms of the numerator and denominator.
- The logarithm of a power is equal to the exponent multiplied by the logarithm of the base.
- The logarithm of 1 is always 0.
- The logarithm of the base to itself is always 1.
| 4. How are logarithms used in real life? | |
Ans. Logarithms have various applications in real life. Some examples include:
- Finance: Logarithms are used in financial calculations, such as compound interest and investment growth.
- Science: Logarithms are used in scientific calculations involving exponential growth or decay, such as in chemistry, physics, and biology.
- Sound and Music: Logarithms are used to measure sound intensity and musical pitch.
- Earthquakes: Logarithms are used to measure the intensity of earthquakes using the Richter scale.
| 5. What is the natural logarithm? | |
Ans. The natural logarithm is a logarithm with base e, where e is an irrational constant approximately equal to 2.71828. The natural logarithm is often denoted as ln(x), and it has various applications in calculus, probability, and exponential growth. It is commonly used when dealing with exponential functions that have the base e.
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Nov 24, 2024 Last updated |
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