Problem
What is the best first step for solving the following equation? \[ \log (2 x-1)+\log (x+4)=1 \] Choose the correct answer below. A. Let $\mathbf{u}=e^{x}$ and write the equation in quadratic form. B. Change to exponential form. C. Take the common logarithm on each side. D. Write the sum of logarithms as the logarithm of a product. E. Take the natural logarithm on each side. F. Use the product rule for exponents.
Solution
Step 1 ：The equation contains two logarithms on the left side. The best first step would be to combine these two logarithms into one. This can be done by using the property of logarithms that states the sum of two logarithms is equal to the logarithm of the product of their arguments.
Step 2 ：Therefore, the correct answer is D. Write the sum of logarithms as the logarithm of a product.
Step 3 ：Final Answer: \(\boxed{\text{(D)}}\)
