what is the approximate value of q in the equation below?\nq + log₂6 = 2q + 2\n-1.613\n-1.522\n0.585\n3.079

Explanation:

Step1: Isolate terms with q

Move terms involving q to one - side. $q+\log_26 = 2q + 2$ can be rewritten as $q-2q=2 - \log_26$.

Step2: Simplify left - hand side

Combine like terms on the left - hand side. $-q=2-\log_26$.

Step3: Evaluate $\log_26$

We know that $\log_26=\frac{\ln6}{\ln2}\approx\frac{1.79176}{0.69315}\approx2.585$.

Step4: Calculate q

Substitute the value of $\log_26$ into the equation $-q = 2-\log_26$. $-q=2 - 2.585=-0.585$. Then $q = 0.585$.

Answer:

0.585