Solving Exponential and Logarithmic Equations

An exponential equation is an equation in which a variable appears in the exponent. For example, 2^x = 8.

A logarithmic equation is an equation that involves a logarithm of a variable. For example, log_b(x) = y means b^y = x.

The natural logarithm, denoted as ln(x), is the logarithm to the base e, where e is approximately 2.718.

The change of base formula states that log_b(a) = log_k(a) / log_k(b) for any positive k.

If ln(a) = ln(b), then a = b, provided a and b are positive.

log_b(mn) = log_b(m) + log_b(n). This property states that the logarithm of a product is the sum of the logarithms.

log_b(m/n) = log_b(m) - log_b(n). This property states that the logarithm of a quotient is the difference of the logarithms.

log_b(m^n) = n * log_b(m). This property states that the logarithm of a power is the exponent times the logarithm of the base.

To solve log_b(x) = c, rewrite it in exponential form: x = b^c.

The domain of a logarithmic function is the set of positive real numbers (x > 0).