Divide both side by $50$ first.
Then undo the powers on both sides.

$(x^{2/3})^{3/2}= 2^{3/2}$

Combine the terms on the left side into one log.

$\text{log}_3((x + 1)(x)) =\text{log}_312$
$(x + 1)(x) = 12$

Divide by $50$ first.
Then take the log of both sides, bringing the $x$ down in front.
Solve for $x$.

This problem is similar to part (b).