If ₂ x+ ₄ x+ _y x+ ₁₆ x- 25 36 and x=2^k , then k is

Step-by-step solution

aligned & ₂ x+ ₄ x+ ₈ x+ ₁₆ x= 25 36 & x 2 + x 4 + x 8 + x 16 = 25 36 & x 2 + x 2 2 + x 3 2 + x 4 2 = 25 36 & x 2 [1+ 1 2 + 1 3 + 1 4 ]= 25 36 & x 2 [ 25 12 ]= 25 36 & 25 12 ₂ x= 25 36 & ₂ x= 1 3 & x=2^ 1 3 & aligned But x=2^ k ... [Given] k = 1 3