Let’s solve both of these logarithmic problems.

Problem 1:

Expression: $2^{\log 4} + 2^{\log 12} - 2^{\log 6}$

Using the property $a^{\log_b x} = x^{\log_b a}$ (or simply $a^{\log a} = x$) for base $a = 2$, we simplify:

1. $2^{\log 4} = 4$
2. $2^{\log 12} = 12$
3. $2^{\log 6} = 6$

Now, substitute these values into the expression: $4 + 12 - 6 = 10$

Thus, the value of the expression is 10.

Problem 2:

Given: $2^{\log a} = 7$

We use the same property again. For base $2$, this simplifies to: $a = 7$

Therefore, the value of $a$ is 7.

Would you like any more details or have further questions?

Here are 5 related questions:

1. How do logarithmic properties simplify calculations?
2. Can logarithmic equations be applied to other bases?
3. How do exponentials and logarithms relate to each other in functions?
4. What are some real-world applications of logarithmic equations?
5. How do we solve logarithmic inequalities?

Tip: Remember that logarithmic functions are the inverses of exponential functions, which makes them powerful tools in simplifying complex equations.