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Observations Related to Logarithmic and Exponential Functions Video Lecture | Mathematics (Maths) Class 12 - JEE
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FAQs on Observations Related to Logarithmic and Exponential Functions Video Lecture - Mathematics (Maths) Class 12 - JEE
| 1. What are logarithmic functions? |  |
Ans. Logarithmic functions are mathematical functions that are the inverse of exponential functions. They are used to solve equations involving exponential growth or decay. In a logarithmic function, the variable appears in the exponent, and the logarithm of a number is the exponent to which another fixed value, called the base, must be raised to produce that number.
| 2. How do logarithmic functions relate to exponential functions? | |
Ans. Logarithmic functions are the inverse of exponential functions. This means that if we have an exponential function of the form y = a^x, the corresponding logarithmic function is given by x = log_a(y). Logarithmic functions help us solve equations involving exponential growth or decay and can be used to find the unknown exponent.
| 3. What are the properties of logarithmic functions? | |
Ans. Logarithmic functions have several properties, including:
- The logarithm of a product is equal to the sum of the logarithms of the individual factors: log_a(xy) = log_a(x) + log_a(y).
- The logarithm of a quotient is equal to the difference of the logarithms of the numerator and denominator: log_a(x/y) = log_a(x) - log_a(y).
- The logarithm of a power is equal to the exponent multiplied by the logarithm of the base: log_a(x^k) = k * log_a(x).
- The logarithm of the base itself is equal to 1: log_a(a) = 1.
These properties help simplify logarithmic expressions and solve equations involving logarithmic functions.
| 4. What are exponential functions? | |
Ans. Exponential functions are mathematical functions where the variable appears as an exponent. They model situations of exponential growth or decay, where the rate of change is proportional to the current value. Exponential functions have a base, which is a positive constant, and the variable is raised to the power of the base.
| 5. How are exponential functions used in real-life applications? | |
Ans. Exponential functions are widely used in various real-life applications, including population growth, compound interest, radioactive decay, and drug dosage calculations. They help model situations where the quantity increases or decreases exponentially over time. For example, exponential functions are used in finance to calculate compound interest, in biology to model population growth, and in physics to describe radioactive decay.
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Dec 22, 2024 Last updated |
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