Question

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

Answer 1

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

Answer 2

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