Let me analyze and solve the problem from the uploaded image.

The problem is:

$3^{\log_3 15} + 10^{\log_{10} 50}$

Step 1: Simplify $3^{\log_3 15}$

Using the logarithmic property:

$a^{\log_a x} = x$

We can simplify $3^{\log_3 15}$ directly to:

$15$

Step 2: Simplify $10^{\log_{10} 50}$

Using the same logarithmic property:

$10^{\log_{10} 50} = 50$

Step 3: Add the results

Now, add the two simplified terms:

$15 + 50 = 65$

Final Answer:

The simplified result is:

$\boxed{65}$

Do you have any questions or need more clarification? Here are some additional questions you might explore:

1. How does the property $a^{\log_a x} = x$ work?
2. Can you apply this to logarithms with other bases?
3. What are some real-world applications of logarithmic simplifications like this one?
4. How do logarithmic identities relate to exponential functions?
5. What happens if the logarithmic argument or base is a fraction?

Tip: Always remember the key property $a^{\log_a x} = x$, which is fundamental in simplifying such expressions.