Answer :

Let's solve the equation step-by-step:

Given:
[tex]\[\log_2 4 + \log_2 4 + \log_2 x = 6\][/tex]

1. Simplify the logarithmic terms:
We know that:
[tex]\[\log_2 4 = 2\][/tex]
because [tex]\(2^2 = 4\)[/tex].

So, we can replace [tex]\(\log_2 4\)[/tex] with 2:
[tex]\[2 + 2 + \log_2 x = 6\][/tex]

2. Combine the constants:
Adding the constant terms:
[tex]\[2 + 2 = 4\][/tex]

So now the equation becomes:
[tex]\[4 + \log_2 x = 6\][/tex]

3. Isolate the logarithmic term:
To isolate [tex]\(\log_2 x\)[/tex], subtract 4 from both sides of the equation:
[tex]\[\log_2 x = 6 - 4\][/tex]

4. Simplify the right side:
[tex]\[\log_2 x = 2\][/tex]

5. Rewrite the logarithmic equation in exponential form:
By definition of logarithms, if [tex]\(\log_b y = z\)[/tex], then [tex]\(b^z = y\)[/tex]. Thus:
[tex]\[2^2 = x\][/tex]

6. Calculate the value:
[tex]\(2^2 = 4\)[/tex].

Therefore, the value of [tex]\(x\)[/tex] is:
[tex]\[ \boxed{4} \][/tex]