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Important Formulae: Logarithms | General Aptitude for GATE - Mechanical Engineering PDF Download
Logarithm
- Log(ab) = Log(a) + Log(b)
- Log(a/b) = Log(a) - Log(b)
- Log(an) = nLog(a)
- Logb b = 1
- Logb 1 = 0
- Logb bx = x
- Ln x means loge x
- x = blogbx
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FAQs on Important Formulae: Logarithms - General Aptitude for GATE - Mechanical Engineering
| 1. What is the formula to find the logarithm of a number? |  |
Ans. The formula to find the logarithm of a number is:
logₐ(x) = y, where a is the base, x is the number, and y is the logarithm.
| 2. How do I solve logarithmic equations? | |
Ans. To solve logarithmic equations, follow these steps:
1. Rewrite the equation using the properties of logarithms.
2. Simplify the equation by combining like terms or using exponentiation.
3. Solve for the variable using algebraic methods.
4. Check the solution by substituting it back into the original equation.
| 3. What are the properties of logarithms? | |
Ans. The properties of logarithms are as follows:
- Product Rule: logₐ(xy) = logₐ(x) + logₐ(y)
- Quotient Rule: logₐ(x/y) = logₐ(x) - logₐ(y)
- Power Rule: logₐ(x^y) = y * logₐ(x)
- Change of Base Rule: logₐ(x) = logᵦ(x) / logᵦ(a)
| 4. How can I evaluate logarithmic expressions without a calculator? | |
Ans. To evaluate logarithmic expressions without a calculator, you can use the properties of logarithms and the known values of common logarithms (logarithms with base 10) and natural logarithms (logarithms with base e). By simplifying the expression using the properties and substituting the known values, you can find the approximate value of the logarithm.
| 5. What are some real-life applications of logarithms? | |
Ans. Logarithms have various real-life applications, including:
- Measuring sound intensity using the decibel scale.
- Calculating earthquake magnitudes using the Richter scale.
- Modeling population growth and decay.
- Analyzing exponential growth and decay in financial investments.
- Determining pH levels in chemistry and acidity/alkalinity of substances.
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