Solving 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 $$log_b(x) = y$$ .

The change of base formula states that $$log_b(a) = \frac{log_k(a)}{log_k(b)}$$ for any positive base $$k$$ .

x = 4.

An exponential equation is an equation in which a variable appears in an exponent, such as $$a^x = b$$ .

x = 9.58.

The product rule states that $$log_b(mn) = log_b(m) + log_b(n)$$ .

The quotient rule states that $$log_b(m/n) = log_b(m) - log_b(n)$$ .

x = 15.

The power rule states that $$log_b(m^p) = p \cdot log_b(m)$$ .

Logarithms and exponentials are inverse functions; if $$y = log_b(x)$$ , then $$b^y = x$$ .