the solution to the equation $log_{2}x + log_{2}(x - 6) = 4$ is $x = \\square$

Explanation:

Step1: Combine log terms via product rule

$\log_2\left[x(x-6)\right] = 4$

Step2: Convert to exponential form

$x(x-6) = 2^4$

Step3: Simplify and rearrange to quadratic

$x^2 - 6x - 16 = 0$

Step4: Factor the quadratic equation

$(x-8)(x+2) = 0$

Step5: Solve for x and check domain

$x=8$ or $x=-2$; discard $x=-2$ since $\log_2(-2)$ is undefined.

Answer:

$8$