What is the base of the natural logarithm?

The base of the natural logarithm is the mathematical constant $$e$$ , approximately equal to 2.718.

Expand the expression: $$\text{log}(4x)$$

$$\text{log}(4) + \text{log}(x)$$ .

What is the definition of the base of a logarithm?

The base of a logarithm is the number that is raised to a power to obtain a certain value. For example, in $$\text{log}_b(x)$$ , $$b$$ is the base.

What is the relationship between logarithms and exponents?

Logarithms are the inverse operations of exponentiation. If $$b^y = x$$ , then $$\text{log}_b(x) = y$$ .

What is the significance of the logarithm of 1?

The logarithm of 1 in any base is always 0, since any number raised to the power of 0 equals 1: $$\text{log}_b(1) = 0$$ .

Properties of Logs & Log Equations Flashcards

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