1. **State the problem:** Solve the equation $25(2^{\log x}) = x$ for $x$. 2. **Recall the properties:** Here, $\log$ denotes the logarithm base 10. We use the property $a^{\log b} = b^{\log a}$ for positive $a,b$. 3. **Rewrite the expression:** Using the property, rewrite $2^{\log x}$ as $x^{\log 2}$. 4. **Substitute:** The equation becomes $$25 \cdot x^{\log 2} = x.$$ 5. **Divide both sides by $x^{\log 2}$ (assuming $x>0$):** $$25 = \frac{x}{x^{\log 2}} = x^{1 - \log 2}.$$ 6. **Take logarithm base 10 on both sides:** $$\log 25 = (1 - \log 2) \log x.$$ 7. **Calculate known logs:** $\log 25 = \log (5^2) = 2 \log 5 \approx 2 \times 0.69897 = 1.39794$ $\log 2 \approx 0.30103$ 8. **Solve for $\log x$:** $$\log x = \frac{\log 25}{1 - \log 2} = \frac{1.39794}{1 - 0.30103} = \frac{1.39794}{0.69897} = 2.$$ 9. **Find $x$:** $$x = 10^{\log x} = 10^2 = 100.$$ **Final answer:** $x = 100$