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Rules of Logarithmic Functions Video Lecture | Mathematics (Maths) Class 12 - JEE
FAQs on Rules of Logarithmic Functions Video Lecture - Mathematics (Maths) Class 12 - JEE
| 1. What are the basic properties of logarithmic functions? |  |
Ans. The basic properties of logarithmic functions are as follows:
- The logarithm of a product is equal to the sum of the logarithms of the individual factors. This property is known as the product rule.
- The logarithm of a quotient is equal to the difference of the logarithms of the numerator and denominator. This property is known as the quotient rule.
- The logarithm of a power is equal to the product of the exponent and the logarithm of the base. This property is known as the power rule.
- The logarithm of 1 to any base is always 0.
- The logarithm of any number to the base of that number is always 1.
| 2. How do I solve logarithmic equations? | |
Ans. To solve logarithmic equations, you can follow these steps:
1. Determine if the equation can be rewritten in logarithmic form.
2. Apply the properties of logarithms to simplify the equation.
3. Solve the resulting equation using algebraic techniques.
4. Check the solution(s) in the original equation to ensure they are valid.
| 3. Are there any restrictions on the domain of logarithmic functions? | |
Ans. Yes, there are restrictions on the domain of logarithmic functions. Since the logarithm of a negative number is undefined in the real number system, the argument of a logarithm must be greater than zero. Therefore, the domain of a logarithmic function is all positive real numbers.
| 4. Can logarithmic functions be used to solve exponential equations? | |
Ans. Yes, logarithmic functions can be used to solve exponential equations. The basic idea is to take the logarithm of both sides of the equation, which allows you to bring the variable out of the exponent. By applying the properties of logarithms, you can then solve for the variable.
| 5. How can logarithmic functions be applied in real-life situations? | |
Ans. Logarithmic functions have various applications in real-life situations, such as:
- Measuring the intensity of earthquakes using the Richter scale, which is based on logarithmic functions.
- Calculating the pH level of a solution in chemistry, which is determined by the concentration of hydrogen ions using a logarithmic scale.
- Modeling population growth or decay in biology and economics.
- Analyzing sound levels, decibels, and musical pitch.
- Calculating the time it takes for a radioactive substance to decay.
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