SOLUTION: Find the value of X, (X²⁰²¹+X²⁰²¹+X²⁰²¹)/X²⁰²⁰ = 30

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Question 1206799: Find the value of X,
(X²⁰²¹+X²⁰²¹+X²⁰²¹)/X²⁰²⁰ = 30
Found 5 solutions by ikleyn, MathTherapy, greenestamps, math_tutor2020, Edwin McCravy:
Answer by ikleyn(52781) About Me  (Show Source):
You can put this solution on YOUR website!
.
Find the value of x     %28X%5E2021+%2B+X%5E2021+%2B+X%5E2021%29%2FX%5E2020 = 30
~~~~~~~~~~~~~~~~~~~~ 

The given equation is equivalent to

    3X = 30

     X = 30%2F3 = 10.


ANSWER.  X = 10.

Solved.

Level of complexity is of   2*2 = 4.


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Comment from student : Thanks but I still don't understand what happened to the denominator X²⁰²⁰


My response : It could be unclear before I posted my solution to you;

                      but after that,  it must be clear that   X%5E2020   in the denominator was canceled with   X%5E2020   in the numerator.



Answer by MathTherapy(10552) About Me  (Show Source):
You can put this solution on YOUR website!
Find the value of X,
(X²⁰²¹+X²⁰²¹+X²⁰²¹)/X²⁰²⁰ = 30


(x²⁰²¹ + x²⁰²¹ + x²⁰²¹)/x²⁰²⁰ = 30

Answer by greenestamps(13200) About Me  (Show Source):
You can put this solution on YOUR website!


Divide each term in the numerator by the denominator and simplify:



Each term in parentheses is equal to

x%5E%282021-2020%29=x%5E1=x

Then

x%2Bx%2Bx=30
3x=30
x=10

Answer by math_tutor2020(3817) About Me  (Show Source):
You can put this solution on YOUR website!

Let w+=+x%5E%282020%29

Multiply both sides by x
wx+=+x%5E%282020%29%2Ax+=+x%5E%282020%2B1%29+=+x%5E%282021%29


The original equation can be rewritten like this
%28wx%2Bwx%2Bwx%29%2F%28w%29+=+30

%283wx%29%2F%28w%29+=+30

3x+=+30
At this point it's fairly easy to see that x = 10.

Answer by Edwin McCravy(20055) About Me  (Show Source):
You can put this solution on YOUR website!

Find the value of x:

%28X%5E2021+%2B+X%5E2021+%2B+X%5E2021%29%2FX%5E2020%22%22=%22%2230

You see that all 3 terms in the numerator are the same, right?

So we have:

%283%2AX%5E2021%29%2FX%5E2020%22%22=%22%2230

You know that to divide exponentials with the same base we subtract their
exponents and keep the same base, right?

So we subtract the exponents 2021-2020, right?

3%2AX%5E%282021-2020%29%22%22=%22%2230

The exponent of x is now just 1, right?

3%2AX%5E1%22%22=%22%2230

We don't have write a 1 exponent, right?

3%2AX%22%22=%22%2230

Divide both sides by 3

x%22%22=%22%2210.

So your question was "What happened to the 2020 exponent in the denominator"? 

The answer is that it got subtracted from the exponent 2021 in the numerator
and that left an exponent of only 1.

Edwin