#1**+1 **

3 ^{x^2 - 42} = 1 / 3^{x}

Note that the term on the right side can be written as 3^{-x}

So we have

3 ^{x^2 - 42} = 3 ^{-x}

Since the bases are the same, we can solve for the exponents

x^2 - 42 = - x add x to both sides

x^2 + x - 42 = 0 factor

( x + 7) ( x - 6) = 0

Setting each factor to 0 and solving for x produces the integer solutions

x = -7 or x = 6

CPhill Dec 19, 2018