1. The problem is to understand what a logarithm is and how to work with it. 2. A logarithm answers the question: to what power must we raise a base number to get another number? The logarithm formula is: $$\log_b(a) = c \iff b^c = a$$ where $b$ is the base, $a$ is the result, and $c$ is the exponent. 3. Important rules of logarithms include: - $\log_b(xy) = \log_b(x) + \log_b(y)$ - $\log_b(\frac{x}{y}) = \log_b(x) - \log_b(y)$ - $\log_b(x^r) = r \log_b(x)$ - Change of base formula: $\log_b(a) = \frac{\log_k(a)}{\log_k(b)}$ for any positive $k \neq 1$ 4. For example, to find $\log_2(8)$, we ask: $2^c = 8$? Since $2^3 = 8$, then $\log_2(8) = 3$. 5. Logarithms are useful for solving equations where the unknown is an exponent, and for simplifying multiplication and division into addition and subtraction. This explanation covers the basics of logarithms and their properties.