1. The problem is to find the value of $x$ in the equation $$5^x = 120$$. 2. To solve for $x$, we use logarithms. The key formula is: $$x = \log_b(a) = \frac{\log(a)}{\log(b)}$$ where $b$ is the base of the exponential and $a$ is the number on the right side. 3. Let's analyze Hawkar's solution: - He writes $\log 5^x = \log 120$, which is correct. - Then he writes $\log 5^x = 12$, which is incorrect because $\log 120 \neq 12$. - Then he writes $x \log 5 = 12$, which follows from the previous incorrect step. - Finally, he writes $x = \frac{12}{\log 5}$, which is incorrect due to the wrong value 12. 4. Malik's solution: - Starts with $5^x = 120$. - Writes $\log_5(120) = x$, which is correct by definition. - Then writes $x = \frac{\log 120}{\log 5}$, which is the correct change of base formula. 5. Therefore, Malik's solution is correct. 6. The correct value of $x$ is: $$x = \frac{\log 120}{\log 5}$$ where $\log$ is the logarithm in any consistent base (commonly base 10 or natural log). 7. To summarize: - Hawkar made a mistake by assigning $\log 120 = 12$, which is false. - Malik correctly applied the logarithm and change of base formula. Final answer: $$x = \frac{\log 120}{\log 5}$$