How do you solve 3(x+1)^(4/3)=48 ?

1 Answer
May 7, 2016

x=7

Explanation:

3(x+1)^(4/3)=48

Divide both sides by color(red)(3)

3(x+1)^(4/3)/color(red)(3)=48/color(red)(3)

(x+1)^(4/3)=16

We know that 2^4=16

=>(x+1)^(4/3)=2^4

Find the 4th root of the equation:

=>(x+1)^(4/3xxcolor(red)(1/4))=2^(4xxcolor(red)(1/4))

=>(x+1)^(1/3)=2

Now, we find the cube of the equation:

=>(x+1)^(color(red)(3)/3)=2^color(red)(3)

=>x+1=2^3

=>x+1=8

Subtract 1 from both sides

=>x+1color(red)(-1)=8color(red)(-1)

=>x=7

Always check your answer:

3(x+1)^(4/3)

=3(7+1)^(4/3)

=3(8)^(4/3)

=3xx2^4 because, color(red)(8^(1/3)=root(3)8=2)

=3xx16

=48

Therefore, x=7