Over ℚ, the unique solution x = 2 is obvious while over ℝ, we have the extra solution x = -2log₅2 : Indeed, changing all bases to 5, putting α = log₅2 and raising to the power of x on both sides forms an index of 5 in a quadratic of x with sum of zeroes -4α + (2 + 2α) thus yielding the extra solution x = -2α = -2log₅2.
2
2
Over ℚ, the unique solution x = 2 is obvious while over ℝ, we have the extra solution x = -2log₅2 : Indeed, changing all bases to 5, putting α = log₅2 and raising to the power of x on both sides forms an index of 5 in a quadratic of x with sum of zeroes -4α + (2 + 2α) thus yielding the extra solution x = -2α = -2log₅2.
By inspection x = 2