1. **State the problem:** Express the equation $2^x + 7 = 57$ in logarithmic form. 2. **Rewrite the equation:** Subtract 7 from both sides to isolate the exponential term: $$2^x = 57 - 7$$ $$2^x = 50$$ 3. **Recall the logarithmic form:** The logarithmic form of $a^x = b$ is: $$x = \log_a b$$ 4. **Apply the formula:** Here, $a=2$ and $b=50$, so: $$x = \log_2 50$$ 5. **Change of base formula:** Since calculators usually use base 10 or $e$, use the change of base formula: $$x = \frac{\log 50}{\log 2}$$ 6. **Interpretation:** This means $x$ is the power to which 2 must be raised to get 50. **Final answer:** $$x = \frac{\log 50}{\log 2}$$ This corresponds to option (a).