What is the value of X in this Problem ? 

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Ok for generality: very neat and precise. I would have straight up taken the log base 3 since the beginning, provided we had found that the 1st member of the equation was 3^4x...

Incomplete. Because log base 3 of 2 implies another variable: 3^y = 2. So your answer begs the question of what y represents.

I guessed 2/5 based on 1/2 being too big and 1/3 being too small. The final answer in decimal form is .4075, so go guessing!!!