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anonymous

  • one year ago

If 10^x equals 0.1 percent of 10^y, where x and y are integers, which of the following must be true? A. y=x+2 B. y=x+3 C. x=y+3 D. y=1,000x E. x=1,000y

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  1. kropot72
    • one year ago
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    The given relationship between x and y can be expressed as \[\large 10^{x}=\frac{10^{y}}{1000}\ .........(1)\] Does that make sense as a first step towards a solution?

  2. anonymous
    • one year ago
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    hmmmm.... why?

  3. anonymous
    • one year ago
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    wait nvm i get it

  4. anonymous
    • one year ago
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    please go on

  5. anonymous
    • one year ago
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    wait why is the 1 at the end? what is that?

  6. kropot72
    • one year ago
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    To find 0.1% of a quantity, we divide the quantity by 1000. The (1) at the end is simply a reference number for this equation. We need to use equation (1) to form another equation.

  7. anonymous
    • one year ago
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    okay

  8. kropot72
    • one year ago
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    Next step is to take logs of both sides of equation (1). Please do that and post your result.

  9. anonymous
    • one year ago
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    Hey we don't use logs for this question

  10. kropot72
    • one year ago
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    Who says we don't use logs?

  11. anonymous
    • one year ago
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    The GRE book I'm using ... There isn't any logs at all

  12. kropot72
    • one year ago
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    Does the book suggest a method of solving that doesn't use logs?

  13. anonymous
    • one year ago
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    well the solutio|dw:1436987482723:dw|n is this but i don't understand it....

  14. kropot72
    • one year ago
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    I understand the method which gives a correct result. It expresses 1/1000 as \[\large \frac{1}{1000}=\frac{1}{10^{3}}=10^{-3}\] Do you understand this step?

  15. kropot72
    • one year ago
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    So equation (1) now becomes \[\large 10^{x}=10^{y} \times 10^{-3}\ ......(2)\]

  16. kropot72
    • one year ago
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    Now we use the rule of indices \[\large a^{b} \times a^{c}=a^{b+c}\] to turn equation (2) into \[\large 10^{x}=10^{y-3}\ .............(3)\] which get the result that x = y - 3 ............(4)

  17. kropot72
    • one year ago
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    Equation (4) can be rearranged to make one of the given answer choices.

  18. kropot72
    • one year ago
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    @yomamabf Please ask if you need more explanation for any steps.

  19. kropot72
    • one year ago
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    |dw:1436988747445:dw| Please note the corrections to the drawing.

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