Answer :
Given:
The given equation is [tex]q+\log _{2}(6)=2 q+2[/tex]
We need to determine the approximate value of q.
Value of q:
To determine the value of q, let us solve the equation for q.
Hence, Subtracting [tex]\log _{2}(6)[/tex] on both sides of the equation, we get;
[tex]q=2 q+2-\log _{2}(6)[/tex]
Subtracting both sides of the equation by 2q, we have;
[tex]-q=2-\log _{2}(6)[/tex]
Dividing both sides of the equation by -1, we have;
[tex]q=\log _{2}(6)-2[/tex]
Now, substituting the value of [tex]log_2(6)=2.585[/tex], we have;
[tex]q=2.585-2[/tex]
Subtracting the values, we get;
[tex]q=0.585[/tex]
Thus, the approximate value of q is 0.585
Hence, Option C is the correct answer.