Evaluate 3( log base 9 of x)^2=6 log base 9 of x

$3 {\log_{9}}^{2} (x) = 6 \log_{9} (x)$

Remove parentheses.

$3 {\log_{9}}^{2} (x) = 6 \log_{9} (x)$

Simplify $6 \log_{9} (x)$ by moving $6$ inside the logarithm.

$3 {\log_{9}}^{2} (x) = \log_{9} (x^{6})$

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

$x = 1$