If 5^x – 5^(x- 3) = 124*5^y, what is y in terms of x?

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If 5^x – 5^(x- 3) = 124*5^y, what is y in terms of x? [#permalink]

11 Feb 2011, 03:17

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If 5^x – 5^(x- 3) = 124*5^y, what is y in terms of x?

A. x
B. x - 6
C. x - 3
D. 2x + 3
E. 2x + 6

[Reveal] Spoiler: OA

Last edited by Bunuel on 20 Sep 2012, 14:15, edited 1 time in total.

Renamed the topic and edited the question.

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Re: ps [#permalink]

11 Feb 2011, 05:13

alltimeacheiver wrote:

If 5x – 5x - 3 = (124)(5y), what is y in terms of x?
A. x
B. x - 6
C. x - 3
D. 2x + 3
E. 2x + 6
Answer:

Question should read:

If 5^x – 5^(x- 3) = 124*5^y, what is y in terms of x?
A. x
B. x - 6
C. x - 3
D. 2x + 3
E. 2x + 6

5^x-5^{x-3}=124*5^y --> factor out 5^{x-3}: 5^{x-3}(5^3-1)=124*5^y --> 5^{x-3}=5^y --> bases are equal so we can equate the powers: y=x-3.

Answer: C.

alltimeacheiver format the questions correctly.
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Re: ps [#permalink]

18 Feb 2011, 12:17

u can also plug in x=3. makes it very simple.
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Re: ps [#permalink]

20 Sep 2012, 14:05

Bunuel wrote:

alltimeacheiver wrote:

If 5x – 5x - 3 = (124)(5y), what is y in terms of x?
A. x
B. x - 6
C. x - 3
D. 2x + 3
E. 2x + 6
Answer:

Hi Bunuel,
I', trying to understand your factorization, but I find some troubles when I have to factorize some value with exponent an expression like in the question (x-3 or x+4),
Could you explain me that or do you have a deck where I could dive into this argument?
Thank you in advance

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Re: ps [#permalink]

20 Sep 2012, 14:14

mario1987 wrote:

Bunuel wrote:

alltimeacheiver wrote:

If 5x – 5x - 3 = (124)(5y), what is y in terms of x?
A. x
B. x - 6
C. x - 3
D. 2x + 3
E. 2x + 6
Answer:

5^{x-3}(5^3-1)=124*5^y --> 5^{x-3+3}-5^{x-3}=124*5^y --> 5^{x}-5^{x-3}=124*5^y.

Theory: math-number-theory-88376.html

Practice:
tough-and-tricky-exponents-and-roots-questions-125956.html
tough-and-tricky-exponents-and-roots-questions-125967.html

Hope it helps.
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If 5^x – 5^(x- 3) = 124*5^y, what is y in terms of x? [#permalink]

12 Dec 2012, 19:52

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{5^{x}}\frac{124}{125}=124(5^y)
5^{x}=5^{y+3}
x=y+3-->y=x-3

Answer: C

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If 5^x – 5^(x- 3) = 124*5^y, what is y in terms of x? [#permalink]

13 Dec 2012, 03:25

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vaivish1723 wrote:

5^x – 5^(x- 3) = (124)(5^y), what is y in terms of x?
A. x
B. x - 6
C. x - 3
D. 2x + 3
E. 2x + 6

Oa is

[Reveal] Spoiler:

Finding one variable in terms of another is very simple. Assume a value for one and find the other. Then look for the option that works.

Say, x = 3 (so that x-3 becomes 0 and we are left with simple calculations)

5^3 - 5^{3- 3} = (124)(5^y)
1 = 5^y
y = 0

Now put x = 3 in the options and find out which option gives you y = 0. Only C does so answer is (C)
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If 5^x – 5^(x- 3) = 124*5^y, what is y in terms of x? [#permalink] 13 Dec 2012, 03:25

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If 5^x – 5^(x- 3) = 124*5^y, what is y in terms of x?

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