What is the solution of the equation 3^5 sqrt (x+2) ^3+3=27?

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

(x + 2) ^ (3/2) = 24 / 243

x + 2 = [ 24 / 243 ]^ (2/3)

x + 2 = [ 8 / 81 ]^ (2/3)

x = [ 4 / 81^ (2/3) ] - 2 = - 1.786

the answer is x=-1.786

We rewrite the function:

(3 ^ 5) * (sqrt (x + 2) ^ 3 + 3) = 27

(3 ^ 5) * (sqrt (x + 2) ^ 3) = 27-3

(3 ^ 5) * (sqrt (x + 2) ^ 3) = 24

(3 ^ 4) * (sqrt (x + 2) ^ 3) = 8

((3 ^ 4) * (sqrt (x + 2) ^ 3)) ^ 2 = (8) ^ 2

(3 ^ 8) * (x + 2) ^ 3 = 64

((3 ^ 8) * (x + 2) ^ 3) ^ (1/3) = (64) ^ (1/3)

(3 ^ (8/3)) * (x + 2) = 4

(x + 2) = 4 * (3 ^ (3/8))

x = 4 * (3 ^ (3/8)) - 2

Answer:

the solution of the equation 3 ^ 5 sqrt (x + 2) ^ 3 + 3 = 27 is

x = 4 * (3 ^ (3/8)) - 2