In this question, take 'log' to mean 'log base 5'. Solve the equation log(x^2-5)-log(x) = 2*log(2)

Note that you can not take a positive base log of a negative number.  log₅(x²-5) - log₅(x) = 2log₅(2) => log₅((x²-5)/x) = log₅(4) => (x²-5)/x = 4 => x²- 4x - 5 = 0 => x = -1 or 5 Go back and check original equation. x cannot be -1 since you cannot take the (positive base) log of a negative number, so x has to be 5.