Short Questions (Question 9 – 11) Posted on April 21, 2020 by user Question 9 Solve the equation, log 2 4 x = 1 − log 4 x Solution: log 2 4 x = 1 − log 4 x log 2 4 x = 1 − log 2 x log 2 4 log 2 4 x = 1 − log 2 x 2 2 log 2 4 x = 2 − log 2 x log 2 16 x 2 = log 2 4 − log 2 x log 2 16 x 2 = log 2 4 x 16 x 2 = 4 x x 3 = 4 16 = 1 4 x = ( 1 4 ) 1 3 = 0.62996 Question 10 Solve the equation, log 4 x = 25 log x 4 Solution: log 4 x = 25 log x 4 1 log x 4 = 25 log x 4 1 25 = ( log x 4 ) 2 log x 4 = ± 1 5 log x 4 = 1 5 or log x 4 = − 1 5 4 = x 1 5 4 = x − 1 5 x = 4 5 4 = 1 x 1 5 x = 1024 x 1 5 = 1 4 x = 1 1024 Question 11 Solve the equation, 2 log x 5 + log 5 x = lg 1000 Solution: 2 log x 5 + log 5 x = lg 1000 2. 1 log 5 x + log 5 x = 3 × ( log 5 x ) → 2 + ( log 5 x ) 2 = 3 log 5 x ( log 5 x ) 2 − 3 log 5 x + 2 = 0 ( log 5 x − 2 ) ( log 5 x − 1 ) = 0 log 5 x = 2 or log 5 x = 1 x = 5 2 x = 5 x = 25