SOLUTION: (x+1)^(-3/2)=8 Solve the complex solution

Question 4028: (x+1)^(-3/2)=8
Solve the complex solution
Found 3 solutions by khwang, tangled_mind, Alan3354:
Answer by khwang(438)   (Show Source): You can put this solution on YOUR website!
It is very good that you typed the expression corectly and clearly .
On way
(x+1)^(-3/2)=8
[(x+1)^(-1/2)]3 = 2^3,
So, (x+1)^(-1/2) = 2.
Square on both sides:
(x+1)^(-1) = 4,
Or 1/(x+1) = 4,
So, (x+1) = 1/4,
x = -3/4.
Another way:
Square on both sides:
(x+1)^(-3) = 8^2 = 64 = 2^6,
Take cubic root on both sides:
(x+1)^(-1) = (2^6)^(1/3) = 2^2 =4,
So, x+1 = 1/4, x = -3/4
Check (-3/4 + 1)^(-3/2) = (1/4)^(-3/2) = (1/2)^2*(-3/2)
= (1/2)^(-3) = [(1/2)^(-1)]^3
= 2^3 = 8 (correct)
Kenny
Answer by tangled_mind(3)   (Show Source): You can put this solution on YOUR website!
(x+1)^(-3/2)=8

to put (-3/2) down multiply both sides with ln
ln{(x+1)^(-3/2)}=ln{8}
(-3/2) ln (x+1) = ln 8
(-3/2)(lnx + ln1) = ln 8
ln x = (ln 8 + (3/2)(ln 1))(-2/3)
e^(ln x) = e^((ln 8 + (3/2)(ln 1))(-2/3))
x=(8+(3/2))(-2/3)
x = -19/3 or -6.33333
Answer by Alan3354(69443)   (Show Source): You can put this solution on YOUR website!
(x+1)^(-3/2)=8
--------------
Get the cube root of both sides
(x+1)^(-3/2)=8
(x+1)^(-1/2)=2
Square both sides
(x+1)^(-1 = 4
1/(x+1) = 4
4x + 4 = 1
x = -3/4
------------
That's the principal solution.
Do you want the other 2 also? There are 3 cube roots of 8.

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