Definition of logarithm
The logarithm of a positive number x to the base b is the exponent y to which b must be raised to obtain x.
The logarithm function is denoted by logb(x), where b is the base and x is the argument.
properties:
- The logarithm function has several properties, including the product rule, quotient rule, power rule, and change of base rule.
- The product rule states that the logarithm of the product of two numbers is equal to the sum of their logarithms.
- The quotient rule states that the logarithm of the quotient of two numbers is equal to the difference of their logarithms.
Important Formulas to Remember in these logarithm
Logarithms:
- Definition of Logarithm: $$\log_{a}(b) = c \iff a^c = b$$
- $$\log_{a}(1) = 0$$
- $$\log_{a}(a) = 1$$
- $$\log_{a}(bc) = \log_{a}(b) + \log_{a}(c)$$
- $$\log_{a}\left(\frac{b}{c}\right) = \log_{a}(b) - \log_{a}(c)$$
- $$\log_{a}(b^c) = c\log_{a}(b)$$
- $$\log_{a}(b) = \frac{\log_{c}(b)}{\log_{c}(a)}$$
Properties of Logarithm: