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

1 Answer
May 7, 2016

Answer:

#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#