Solve the equation log3 x + 1/log3 x=5/2 Solution We\'ll multiply all terms both sides by the least common denominator. 2*log3 (x)*log3 (x) + 2 = 5*log3 (x) 2*[log3 (x)]^2 - 5*log3 (x) + 2 = 0 We\'ll replace log3 (x) by t. 2t^2 - 5t + 2 = 0 We\'ll apply quadratic formula: t1 = [5+sqrt(25 - 16)]/4 t1 = (5+3)/4 t1 = 2 t2 = 1/2 But log3 (x)=t. log3 (x)=t1 <=> log3 (x)=2 We\'ll take antilogarithms and we\'ll get: x = 3^2 x = 9 log3 (x)=t2 x = sqrt 3 Since both values are positive, we\'ll accept them as solutions of equation: {sqrt3 ; 9}..