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3
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3^{ x+1 } cdot 2 = 2^{ x-1 } cdot 3 newline
3^{ x+1 } cdot 3^{-1} = 2^{ x-1 } cdot 2^{-1} newline
3^{ x+1-1 } = 2^{ x-1 -1} newline
3^{ x } = 2^{ x-2} newline
{3^{ x }} over {2^{x}} = {2^-2} newline
left({3} over {2}right)^x = {2^-2} newline
ln left({3} over {2}right)^x = ln left( {2^-2} right) newline
x cdot ln left({3} over {2}right) = -2 cdot ln {2} newline
x cdot left( ln {3} - ln {2}right) = -2 cdot ln {2} newline
x = -2 cdot {{ln {2} } over { ln {3} - ln {2}}} newline