If 2 2 x+10 2 x=5 , then x=

Step-by-step solution

Here, 2 2 x+10 2 x=5 We know that, 2 x= 1 2 (e^ 2 x +e^ -2 x ) 2 x= 1 2 (e^ 2 x -e^ -2 x ) So, 2 [ 1 2 (e^ 2 x +e^ -2 x ) ]+10 [ 1 2 (e^ 2 x -e^ -2 x ) ]=5 aligned & e^ 2 x +e^ -2 x +5 e^ 2 x -5 e^ -2 x =5 & 6 e^ 2 x -5-4 e^ -2 x =0 (3 e^ 2 x -4 ) (2 e^ 2 x +1 )=0 aligned e^ 2 x 4 3 or e^ 2 x =- 1 2 The only real solution occurs when e^ 2 x >0 . So, 2 x= 4 3 x= 1 2 4 3