The equation shown in the image is:

$2 \log_4 4^7 = x$

Let's simplify and solve for $x$.

Step 1: Simplify the logarithmic expression

We know from the properties of logarithms that:

$\log_b (a^n) = n \log_b a$

So, apply this rule to $\log_4 4^7$:

$\log_4 4^7 = 7 \log_4 4$

Since $\log_4 4 = 1$ (because $4^1 = 4$), we have:

$\log_4 4^7 = 7 \times 1 = 7$

Step 2: Substitute back into the equation

Now the equation becomes:

$2 \times 7 = x$

$x = 14$

Thus, the solution is $x = 14$.

Would you like more details or have any questions?

Here are 5 related questions to further your understanding:

1. What are the common properties of logarithms, and how do they help simplify expressions?
2. How does the base of a logarithm affect its value, and why is $\log_b b = 1$?
3. What are the steps for solving equations involving logarithms with different bases?
4. How can exponential and logarithmic functions be used to solve real-world problems?
5. Can you solve $3 \log_2 (x^4) = 12$ using similar properties of logarithms?

Tip: Always look for ways to simplify logarithmic expressions using known properties like the power rule or change of base formula.