If ₂ (2^ x-1 +6 )+ ₂ (4^ x-1 )=5 , then x=

Step-by-step solution

We have, aligned & ₂ (2^ x-1 +6 )+ ₂ (4^ x-1 )=5 & . 2^ x-1 +6 ) (2^ 2 x-2 )=2⁵ aligned Let y=2^ x-1 (y+6) y²=2⁵ aligned & y³+6 y²-32=0 & (y-2) (y²+8 y+16 )=0 aligned So, aligned y &=2 2^ x-1 &=2¹ aligned On comparing both sides, we get array r x-1=1 x=2 array