anonymous
  • anonymous
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
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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chestercat
  • chestercat
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kropot72
  • kropot72
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?
anonymous
  • anonymous
hmmmm.... why?
anonymous
  • anonymous
wait nvm i get it

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anonymous
  • anonymous
please go on
anonymous
  • anonymous
wait why is the 1 at the end? what is that?
kropot72
  • kropot72
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.
anonymous
  • anonymous
okay
kropot72
  • kropot72
Next step is to take logs of both sides of equation (1). Please do that and post your result.
anonymous
  • anonymous
Hey we don't use logs for this question
kropot72
  • kropot72
Who says we don't use logs?
anonymous
  • anonymous
The GRE book I'm using ... There isn't any logs at all
kropot72
  • kropot72
Does the book suggest a method of solving that doesn't use logs?
anonymous
  • anonymous
well the solutio|dw:1436987482723:dw|n is this but i don't understand it....
kropot72
  • kropot72
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?
kropot72
  • kropot72
So equation (1) now becomes \[\large 10^{x}=10^{y} \times 10^{-3}\ ......(2)\]
kropot72
  • kropot72
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)
kropot72
  • kropot72
Equation (4) can be rearranged to make one of the given answer choices.
kropot72
  • kropot72
@yomamabf Please ask if you need more explanation for any steps.
kropot72
  • kropot72
|dw:1436988747445:dw| Please note the corrections to the drawing.

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