Wat is de waarde van x in 81 ^ (x ^ 3 + 2x ^ 2) = 27 ^ ((5 * x) / 3)?

Antwoord:

#x = 1/2 of x = -5 / 2 #

Uitleg:

# 81 ^ (x ^ 3 + 2x ^ 2) = 27 ^ ((5x) / 3) #

Notitie: # 3 ^ 4 = 81 en 3 ^ 3 = 27 #

# 3 ^ (4 (x ^ 3 + 2x ^ 2)) = 3 ^ (3 ((5x) / 3)) #

# cancel3 ^ (4 (x ^ 3 + 2x ^ 2)) = cancel3 ^ (3 ((5x) / 3)) #

# 4 (x ^ 3 + 2x ^ 2) = 3 ((5x) / 3) #

# 4 (x ^ 3 + 2x ^ 2) = cancel3 ((5x) / cancel3) #

# 4x ^ 3 + 8x ^ 2 = 5x #

Door te delen door #X#

# (4x ^ 3) / x + (8x ^ 2) / x = (5x) / x #

# (4x ^ (cancel3 ^ 2)) / cancelx + (8x ^ (cancel2 ^ 1)) / cancelx = (5cancelx) / cancelx #

# 4x ^ 2 + 8x = 5 #

# 4x ^ 2 + 8x - 5 = 0 #

Factorisatiemethode gebruiken..

# 2 en 10-> "factoren" #

Bewijs: # 10x - 2x = 8x en 10 xx -2 = -20 #

daarom;

# 4x ^ 2- 2x + 10x - 5 = 0 #

Groeperen van de factoren;

# (4x ^ 2- 2x) + (10x - 5) = 0 #

factoren ontbinden;

# 2x (2x - 1) + 5 (2x - 1) = 0 #

De factoren scheiden;

# (2x - 1) (2x + 5) = 0 #

# 2x - 1 = 0 of 2x + 5 = 0 #

# 2x = 1 of 2x = -5 #

#x = 1/2 of x = -5 / 2 #