x = 78
The equation given is
3[tex](x + 3)^{3/4}[/tex]= 81
first we will divide 3 of the right side to left side number which is 81
i.e 81/3 = 27
So we get the equation
[tex](x + 3)^{3/4}[/tex] =27
We can also write the equation as
[tex](x + 3)^{3/4}[/tex]= [tex]3^{3}[/tex]
[tex][(x + 3)^{1/4]^{3}[/tex]= [tex]3^{3}[/tex]
So from, this we get
[tex](x + 3)^{1/4}[/tex] = 3
Now we have to side with the multiply both power of four(4)
[tex][ (x + 3)^{1/4}]^{4}[/tex]= [tex]3^{4}[/tex]
we get
x + 3 = 81
x = 78
So the value of x is 78.
To know more about the solution of the power equation refer to the link given below:
https://brainly.com/question/28595295
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