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to solve the equation lets change the right side 1 over Square 2 equals square root of 1 over 2. we can write it as 1 over 2 to the power 1 over 2. but 1 over 2 can be written as square root of one over four so we get 1 over 4 to the power one over two then one over two using exponent rule we get one over four to the power one over four now the equation becomes x 12 x equals half compare left side and right side so get x equals one over two we can also write the equation as X to power x equals a quarter to power quarter compare the left side and right side we get x equals one over four so we got two solutions to the given equation