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:
Definition of Logarithm: $$\log_{a}(b) = c \iff a^c = b$$
Properties of Logarithm:
1
$$\log_{a}(1) = 0$$
2
$$\log_{a}(a) = 1$$
2
$$\log_{a}(bc) = \log_{a}(b) + \log_{a}(c)$$
3
$$\log_{a}\left(\frac{b}{c}\right) = \log_{a}(b) - \log_{a}(c)$$
4
$$\log_{a}(b^c) = c\log_{a}(b)$$
6
$$\log_{a}(b) = \frac{\log_{c}(b)}{\log_{c}(a)}$$