1. **Stating the problem:** Understand the relationship between exponents and logarithms. 2. **Definition of exponents:** Exponents represent repeated multiplication. For example, $a^x$ means multiplying $a$ by itself $x$ times. 3. **Definition of logarithms:** 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. **Formula:** The key formula connecting exponents and logarithms is: $$a^x = b \iff \log_a b = x$$ 5. **Important rules:** - The base $a$ must be positive and not equal to 1. - The argument $b$ must be positive. 6. **Example:** If $2^3 = 8$, then $\log_2 8 = 3$. 7. **Explanation:** This means that 2 raised to the power 3 equals 8, so the logarithm base 2 of 8 is 3. This relationship allows us to solve equations involving exponents by converting them into logarithmic form and vice versa.