Solve for x log of x(x+6)=2

$\log (x) (x + 6) = 2$

Simplify $\log (x) (x + 6)$ .

Apply the distributive property.

$\log (x) x + \log (x) \cdot 6 = 2$

Multiply $\log (x) \cdot 6$ .

Reorder $\log (x)$ and $6$ .

$\log (x) x + 6 \cdot \log (x) = 2$

Simplify $6 \cdot \log (x)$ by moving $6$ inside the logarithm.

$\log (x) x + \log (x^{6}) = 2$

Reorder factors in $\log (x) x + \log (x^{6})$ .

$x \log (x) + \log (x^{6}) = 2$

Graph each side of the equation. The solution is the x-value of the point of intersection.

$x \approx 1.80415461$