I am sure that the "x" is not a variable here, that x is "times".Originally Posted byardnas

Here is one way.

3^(n-6) * y^(4n-8) = 1

Divide both sides by 3^(n-6),

y^(4n-8) = 1/ [3^(n-6)]

y^(4n-8) = 3^[-(n-6)]

y^(4n-8) = 3^(6-n) -----------***

So, if (4n-8) = (6-n), then y=3.

4n -8 = 6 -n

4n +n = 6 +8

5n = 14

n = 14/5 = 2.8

Therefore, n=2.8 and y=3. ---------answer.

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There could be infinitely many sets of answer, not only (n=2.8, y=3), but I won't investigate that anymore. I assumed you need at least one set of answers only.

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Check,

3^(n-6) * y^(4n-8) = 1

3^(2.8 -6) * 3^(4*2.8 -8) =? 1

3^(-3.2) * 3^(11.2 -8) =? 1

3^(-3.2) * 3^(3.2) =? 1

3^[(-3.2) +3.2] =? 1

3^0 =? 1

1 =? 1

Yes, so, OK.