How do you solve #3(x+3)^(3/4)= 81#?

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Answer 1 · 2015-04-10T18:56:04

Simply divide by #3#:

#(x+3)^(3/4) = 27#

Raise everything to the #4/3# to multiply by the #3/4# to get #1#:

#x+3 = 27^(4/3)#

And subtract #3#.

#x = 27^(4/3) - 3 = 3^(3*4/3) - 3 = 3^4 - 3 = 78#

To check:
#(78+3) ^(3/4) = 27#
#81^(3/4) = 27#
#3^3 = 27#