To solve the problem of combining $\log 5 + 2\log x$ into a single logarithm, we can use the properties of logarithms outlined in the box. These are:

1. Product Rule: $\log_b(P) + \log_b(Q) = \log_b(PQ)$
2. Power Rule: $a\log_b(P) = \log_b(P^a)$

Step-by-step Solution:

1. Start with the given expression:
   $\log 5 + 2\log x$

2. Apply the Power Rule to $2\log x$:
   $2\log x = \log(x^2)$

   So the expression becomes:
   $\log 5 + \log(x^2)$

3. Apply the Product Rule to combine the terms:
   $\log 5 + \log(x^2) = \log(5 \cdot x^2)$

   Final expression:
   $\log(5x^2)$

Correct Answer:

The correct choice is C: $\log 5x^2$.

Do you want additional explanation or examples?

Related Questions:

1. What is the difference between the product and power rules of logarithms?
2. How can $\log_b(P) - \log_b(Q)$ be simplified using logarithmic rules?
3. What is the expanded form of $\log(x^3y)$?
4. Why are logarithmic properties useful in simplifying equations?
5. How can logarithmic equations be applied to solve real-world problems?

Tip:

Always look for logarithmic rules that simplify the expression step by step, starting with powers before combining terms using products or quotients.