1. The problem is to understand the relationship between exponents and logarithms. 2. Exponents represent repeated multiplication. For example, $a^x = b$ means multiplying $a$ by itself $x$ times equals $b$. 3. Logarithms are the inverse operation of exponents. If $a^x = b$, then the logarithm base $a$ of $b$ is $x$, written as $\log_a b = x$. 4. Important rules: - $\log_a (xy) = \log_a x + \log_a y$ - $\log_a \left(\frac{x}{y}\right) = \log_a x - \log_a y$ - $\log_a (x^r) = r \log_a x$ 5. These rules help simplify expressions involving logarithms and exponents. 6. Example: If $2^3 = 8$, then $\log_2 8 = 3$ because 2 multiplied by itself 3 times equals 8. This shows how exponents and logarithms are inverse functions.