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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, 02:17
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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, 13:15, edited 1 time in total.
Renamed the topic and edited the question.
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Re: ps [#permalink]  11 Feb 2011, 04:13
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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

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: $$y=x-3$$.

alltimeacheiver format the questions correctly.
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Re: ps [#permalink]  18 Feb 2011, 11:17
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u can also plug in x=3. makes it very simple.
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Re: ps [#permalink]  20 Sep 2012, 13:05
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

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: $$y=x-3$$.

alltimeacheiver format the questions correctly.

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?
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Re: ps [#permalink]  20 Sep 2012, 13:14
Expert's post
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

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: $$y=x-3$$.

alltimeacheiver format the questions correctly.

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?

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

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, 18:52
1
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$${5^{x}}\frac{124}{125}=124(5^y)$$
$$5^{x}=5^{y+3}$$
$$x=y+3-->y=x-3$$

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If 5^x – 5^(x- 3) = 124*5^y, what is y in terms of x? [#permalink]  13 Dec 2012, 02:25
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Expert's post
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:
c

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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Re: ps [#permalink]  24 Sep 2013, 08:07
144144 wrote:
u can also plug in x=3. makes it very simple.

Hi,

Can you please tell why you chose only 3 to substitute x with ?
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If 5^x – 5^(x- 3) = 124*5^y, what is y in terms of x? [#permalink]  26 Feb 2014, 19:47
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$$5^x – 5^{(x- 3)} = 124*5^y$$

Re-write as

$$5^x – 5^{(x- 3)} = (125 - 1 ) * 5^y$$

$$5^x – 5^{(x- 3)} = 125* 5^y - 5^y$$

$$5^x – 5^{(x- 3)} = 5^{(y+3)} - 5^y$$

LHS = RHS, so equating the powers

y = x+3 ; Answer = C
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Re: If 5^x – 5^(x- 3) = 124*5^y, what is y in terms of x? [#permalink]  28 Mar 2015, 22:00
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Re: If 5^x – 5^(x- 3) = 124*5^y, what is y in terms of x? [#permalink]  29 Mar 2015, 07:10
Expert's post
alltimeacheiver wrote:
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

Given that 5^x – 5^(x- 3) = 124*5^y
So, 5^(x-3+3) - 5^(x- 3) = 124*5^y
So, 5^(x-3) [5^3 - 1] = 124*5^y
So, 5^(x-3)*124 = 124*5^y
So, 5^(x-3) = 5^y
So, x-3 = y

Hence option (C).

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Re: If 5^x – 5^(x- 3) = 124*5^y, what is y in terms of x?   [#permalink] 29 Mar 2015, 07:10
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