1. **State the problem:** Given the equation $a^b = c$, we want to make $b$ the subject of the formula. 2. **Recall the formula and rules:** The equation involves an exponential expression where $a$ is the base, $b$ is the exponent, and $c$ is the result. 3. **Use logarithms to isolate $b$:** Taking the logarithm of both sides helps us bring down the exponent. $$\log(a^b) = \log(c)$$ 4. **Apply the logarithm power rule:** $$b \log(a) = \log(c)$$ 5. **Solve for $b$ by dividing both sides by $\log(a)$:** $$b = \frac{\log(c)}{\log(a)}$$ 6. **Intermediate step showing cancellation:** $$b = \frac{\cancel{\log(c)}}{\cancel{\log(a)}}$$ (Here, the cancellation indicates division by $\log(a)$ to isolate $b$.) 7. **Final answer:** $$b = \frac{\log(c)}{\log(a)}$$ This formula means that to find the exponent $b$, you take the logarithm of $c$ and divide it by the logarithm of $a$.