Question 1187454
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Solve for x and state any restrictions. 0° ≤ x ≤ 360°
{{{ 27(3^(2tanx)) - 242(3^tanx) - 9 = 0 }}}
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            I came to fix error in the post by  Alan.



Sub z for 3^tan(x)
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27z^2 - 242z - 9 = 0
(27z + 1)*(z - 9) = 0


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z = 9
3^tan(x) = 9
tan(X) = 2


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27z + 1 = 0
z = -1/27
{{{3^tan(x)}}} = -1/27


There is no solution:  the left side is  ALWAYS  positive,  while the right side is  NEGATIVE.
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<U>ANSWER</U>.  x = arctan(2).



Solved.