Lesson: Rewriting Logarithmic Equations

A logarithm is the exponent to which a base must be raised to produce a given number. For example, in the equation $$\text{log}_b(a) = c$$ , it means that $$b^c = a$$ .

$$p = 3^4$$ .

The conversion is done by rewriting it as $$b^y = x$$ .

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

First, rewrite it as $$6^3 = 2x + 3$$ , then solve for $$x$$ to get $$x = 106.5$$ .

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

$$x^3 = 1000$$ .

$$x = 10$$ .

It signifies that any base raised to the power of 0 equals 1, i.e., $$b^0 = 1$$ .

$$8^0 = x$$ , which means $$x = 1$$ .