Logarithmic and Exponential Equations

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

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

$$2^3 = 8$$ .

2, because $$10^2 = 100$$ .

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

$$n = \frac{1}{2}$$ .

5, because $$2^5 = 32$$ .

$$2^{-3} = \frac{1}{8}$$ .

2, because $$4^2 = 16$$ .

An exponential function is a mathematical function of the form $$f(x) = a \times b^x$$ , where $$a$$ is a constant, $$b$$ is the base, and $$x$$ is the exponent.