Logarithms

Logarithm definition and their formulas:

• Logarithms are mathematical functions that are used to express the relationship between two quantities that are being multiplied or divided.
• The logarithm of a number is the exponent to which another fixed value called the base must be raised to produce that number.
• Logarithms have a wide range of applications in mathematics, science, engineering, and finance.
• The most commonly used logarithms are the base-10 logarithm (common logarithm) and the natural logarithm (base e).
• Logarithmic functions are the inverse of exponential functions, and they can be used to solve equations involving exponential functions  
  

Logarithms Formulas:

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Definition of Logarithm: $$\log_{a}(b) = c \iff a^c = b$$

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Properties of Logarithm:

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1

$$\log_{a}(1) = 0$$

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2

$$\log_{a}(a) = 1$$

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2

$$\log_{a}(bc) = \log_{a}(b) + \log_{a}(c)$$

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3

$$\log_{a}\left(\frac{b}{c}\right) = \log_{a}(b) - \log_{a}(c)$$

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4

$$\log_{a}(b^c) = c\log_{a}(b)$$

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6

$$\log_{a}(b) = \frac{\log_{c}(b)}{\log_{c}(a)}$$

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