Solve log 10 2 x + 1 + x = log 10 6 + x log 10 5 .

Step-by-step solution

The given expression is log 10 2 x + 1 + x = log 10 6 + x log 10 5 We know that log m x + log m y = log m x y   &   log m x + log m y = log m x y ⇒ log 10 2 x + 1 = x log 10 5 - log 10 10 + log 10 6 ⇒ log 10 2 x + 1 = - log 10 2 x + log 10 6 ⇒ log 10 2 x + 1 + log 10 2 x = log 10 6 ⇒ log 10 2 x 2 x + 1 = log 10 6 Taking antilog on both sides, we get ⇒ 2 x 2 x + 1 = 6 ⇒ 2 x 2 + 2 x - 6 = 0 ⇒ 2 x - 2 2 x + 3 = 0 ⇒ 2 x = 2 ⇒ x = 1 Hence, x = 1