122 Logaritmos.

Apuntes

• Subtopic: Properties of Logarithms The properties of logarithms are fundamental in simplifying and solving logarithmic expressions. Here are some key properties: 1. The logarithm of a product is the sum of the logarithms: $$\log \, ab = \log \, a + \log \, b.$$ 2. The logarithm of a power is the exponent times the logarithm of the base: $$\log \, a^n = n \, \log \, a.$$ 3. The logarithm of 1 is always 0: $$\log \, 1 = 0.$$ 4. The logarithm of a quotient is the difference of the logarithms: $$\log \, \frac{a}{b} = \log \, a - \log \, b.$$ 5. The logarithm of a root is the reciprocal of the root times the logarithm of the base: $$\log \, \sqrt[n]{a} = \frac{1}{n} \, \log \, a.$$ 6. The logarithm of a number to its own base is 1: $$\log_a \, a = 1.$$