Determine lg x = - lg 2 Solution First of all, we have to set the existence conditions: x>0 The interval of admissible values for x is (0,+inf.) We\'ll use the power property of logarithm: lg x=-lg 2 lg x = lg 2^-1 We\'ll use the property of negative exponent: a^-x = 1/a^x, so 2^-1 = 1/2 lg x = lg 1/2 Because the bases are matching, we\'ll use the one to one property of logarithms: x=1/2>0 Since the value belongs to the interval of admissible values, we\'ll accept the root of the equation x = 1/2..