1. We are asked to find between which two consecutive integers the value of $x$ lies when $2^x = 14$. 2. To solve for $x$, take the logarithm base 2 of both sides: $$x = \log_2(14)$$ 3. Since $14$ is not a power of 2, we estimate $x$ by comparing with powers of 2: - $2^3 = 8$ - $2^4 = 16$ 4. Because $8 < 14 < 16$, it follows that: $$3 < x < 4$$ 5. For a more precise value, use the change of base formula: $$x = \frac{\log(14)}{\log(2)} \approx \frac{1.1461}{0.3010} \approx 3.81$$ 6. Therefore, $x$ lies between the consecutive integers 3 and 4. Final answer: $x$ is between 3 and 4.