SOLUTION: How to solve for x and n. for the equation given below? 2^(n) ⋅ x = 2^(10) ⋅ 500

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Question 1145494: How to solve for x and n. for the equation given below?
2^(n) ⋅ x = 2^(10) ⋅ 500
Found 3 solutions by josgarithmetic, ikleyn, MathTherapy:
Answer by josgarithmetic(39616) About Me  (Show Source):
You can put this solution on YOUR website!
Compare corresponding parts
Nothing to solve

Answer by ikleyn(52776) About Me  (Show Source):
You can put this solution on YOUR website!
.

The left side is  2%5En%2Ax.


The right side is  2%5E10%2A500 = 2%5E10%2A5%2A100 = 2%5E12%2A5%5E3.


Then, comparing the left and the right sides, you get several solutions in integer numbers:


    n = 12,  x = 5%5E3 = 125,

    n = 11,  x       = 250,

    n = 10,  x       = 500,

    n =  9,  x       = 1000,

    n =  8,  x       = 2000,
      
    n =  7,  x       = 4000,

    . . . .  and so on . . .  


    n =  0,  x        = 2%5E0%2A%282%5E12%2A5%5E3%29.

Solved, answered, explained and completed.



Answer by MathTherapy(10551) About Me  (Show Source):
You can put this solution on YOUR website!
How to solve for x and n. for the equation given below?
2^(n) ⋅ x = 2^(10) ⋅ 500
matrix%281%2C3%2C+2%5E%28n%29%28x%29%2C+%22=%22%2C+2%5E%2810%29%28500%29%29

Equating terms, we can say that: matrix%282%2C3%2C+2%5En%2C+%22=%22%2C+2%5E10%2C+%28x%29%2C+%22=%22%2C+%28500%29%29, which results in: highlight_green%28matrix%282%2C3%2C+n%2C+%22=%22%2C+10%2C+x%2C+%22=%22%2C+500%29%29

The right side can also be SIMPLIFIED to: 

Either of the 2 works!!

That's it!!