Løs for x: 16 * 4 ^ (x + 2) - 16 * 2 ^ (x + 1) + 1 = 0?

Svar:

# x = -4 #

Forklaring:

# 16 * 4 ^ (x + 2) - 16 * 2 ^ (x + 1) + 1 = #

# = 16 ^ 2cdot4 ^ x-2cdot16cdot2 ^ x + 1 = #

# = 16 ^ 2cdot (2x) ^ 2-32cdot 2 ^ x + 1 = 0 #

Making # Y = 2 ^ x #

# 16 ^ 2y ^ 2-32y + 1 = 0 # løse for # Y # vi har

#y = 1/16 = 2 ^ x = 2 ^ (- 4) # derefter # x = -4 #