1. The problem is to understand and solve questions related to logarithms. 2. The logarithm function is defined as $\log_b(a) = c$ means $b^c = a$, where $b$ is the base, $a$ is the argument, and $c$ is the exponent. 3. Important rules include: - $\log_b(xy) = \log_b(x) + \log_b(y)$ (product rule) - $\log_b\left(\frac{x}{y}\right) = \log_b(x) - \log_b(y)$ (quotient rule) - $\log_b(x^r) = r \log_b(x)$ (power rule) - Change of base formula: $\log_b(a) = \frac{\log_k(a)}{\log_k(b)}$ for any positive $k \neq 1$ 4. To solve a logarithmic equation, isolate the logarithm and rewrite it in exponential form. 5. Example: Solve $\log_2(x) = 3$ - Using the definition, $2^3 = x$ - So, $x = 8$ 6. Always check the domain: the argument of a logarithm must be positive. This explanation covers the basics and how to solve simple logarithmic equations.