Lesson: Rewriting Logarithmic Equations

A logarithm is the exponent to which a base must be raised to produce a given number. For example, if $$b^y = x$$ , then $$\text{log}_b(x) = y$$ .

The exponential form is $$b^c = a$$ .

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.

Rewrite it in exponential form: $$x = b^c$$ .

The change of base formula is $$\text{log}_b(a) = \frac{\text{log}_k(a)}{\text{log}_k(b)}$$ for any base $$k$$ .

Since $$3^4 = 81$$ , then $$x = 4$$ .

The exponential form is $$2^4 = 16$$ .

Since $$5^2 = 25$$ , then $$\text{log}_5(25) = 2$$ .

$$\text{log}_b(b) = 1$$ because any number raised to the power of 1 is itself.

Rewrite it as $$x^3 = 1000$$ , so $$x = 10$$ .