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

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

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New post 16 Jul 2017, 10:33
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


5^x - 5^x(x-3) = 124*5^y

5^(x-3)*(5^3 - 1) = 124*5^y

5^(x-3)*124 = 124*5^y

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

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New post 16 Oct 2017, 21:03
5^x−5^(x−3)=124∗5^y
5^x−5^(x−3)=(125-1)∗5^y
5^x−5^(x−3)=(5^3-1)*5^y
5^x−5^(x−3)=5^(3+y)-5^y
x=3+y or x-3=y

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

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New post 21 Jan 2018, 04:41
Would you not say this is a 700 question?

Also, the source is Gmat Prep Extension Pack 1 (at least I have found this question here).

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

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New post 11 Mar 2018, 09:19
VeritasPrepKarishma wrote:
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


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)


So what is the mistake in this method:

5^x - 5^(x - 3) = (5^3 - 5^0) * 5^y
5^x - 5^(x - 3) = (5^3 - 1) * 5^y
5^x - 5^(x - 3) = 5^3y - 5^y

3y = x AND y = x-3 - this is enough for correct answer
x = y+3
y + 3 = 3y
y = 1.5
x =4.5


Clearly, something is off with the above, but I have no idea what!
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If 5^x – 5^(x- 3) = 124*5^y, what is y in terms of x?  [#permalink]

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New post 13 Mar 2018, 18:06
Manychips wrote:
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

So what is the mistake in this method:

5^x - 5^(x - 3) = (5^3 - 5^0) * 5^y
5^x - 5^(x - 3) = (5^3 - 1) * 5^y
5^x - 5^(x - 3) = 5^3y - 5^y

3y = x AND y = x-3 - this is enough for correct answer
x = y+3
y + 3 = 3y
y = 1.5
x =4.5


Clearly, something is off with the above, but I have no idea what!

Manychips , the highlighted part should be:
(3 + y) or (y + 3).
\(5^3*5^{y}=5^{(3+y)}\)

Same base, multiplication: add exponents.
You multiplied the exponents.

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

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New post 19 Apr 2018, 12:11
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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


One option is to rewrite the left side of the equation by factoring out 5^(x-3)
So, we get: 5^(x-3)[5^3 - 1] = (124)(5^y)
Evaluate to get: 5^(x-3)[125 - 1] = (124)(5^y)
Simplify to get: 5^(x-3)[124] = (124)(5^y)
Divide both sides by 124 to get: 5^(x-3) = 5^y
So, x-3 = y

Answer: C

-----------------------------------------------------
ASIDE: A lot of students struggle to see how we can factor 5^x - 5^(x-3) to get 5^(x-3)[5^3 - 1]
Sure, they may be okay with straightforward factoring like these examples:
k^5 - k^3 = k^3(k^2 - 1)
m^19 - m^15 = m^15(m^4 - 1)
But they have problems when the exponents are variables.

IMPORTANT: Notice that, each time, the greatest common factor of both terms is the term with the smaller exponent.

So, in the expression 5^x - 5^(x-3), the term with the smaller exponent is 5^(x-3, so we can factor out 5^(x-3)

Likewise, w^x + x^(x+5) = w^x(1 + w^5)
And 2^x - 2^(x-2) = 2^(x-2)[2^2 - 1]
------------------------------------------------------------

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

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New post 19 Apr 2018, 12:12
Top Contributor
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



Another option is to PLUG IN a value for x and see what kind of relationship we get between x and y.
There are two "nice" x-values to plug in. They are x = 0 and x = 3, since we can easily use these to evaluate 5^x and 5^(x-3). Of these two values, x = 3 is the easier one to plug in.
So, let's plug in x = 3
We get: 5^3 - 5^(3-3) = (124)(5^y)
Simplify to get: 125 - 1 = (124)(5^y)
Simplify to get: 124 = (124)(5^y)
Divide both sides by 124 to get: 1 = 5^y
Solve for y to get: y = 0

So, when x = 3, y = 0.

Now we'll check the answer choices to see which one satisfies this relationship.
A) y = x... So, we get 0 = 3 (NOPE)
B) y = x - 6... So, we get 0 = 3 - 6 (NOPE)
C) y = x - 3... So, we get 0 = 3 - 3 IT WORKS!
D) y = 2x + 3... So, we get 0 = 2(3) + 3 (NOPE)
E) y = 2x + 6... So, we get 0 = 2(3) + 6 (NOPE)

Answer: C

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

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New post 03 Oct 2018, 12:02
Hi,

I don't understand how all yall are factoring 5^x-3 out of 5^x-5^x-3 - isn't the only common factor 5^x???? I am getting 5^x(1-5^-3) for the left side of the equation
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Re: If 5^x – 5^(x- 3) = 124*5^y, what is y in terms of x?  [#permalink]

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New post 20 May 2020, 17:21
ScottTargetTestPrep wrote:
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



We can simplify the given equation:

5^x – 5^(x- 3) = 124*5^y

5^x – (5^x)(5^- 3) = 124*5^y

5^x(1 – (5^- 3)) = 124*5^y

5^x(1 – 1/125) = 124*5^y

5^x(1 – 1/125) = 124*5^y

5^x(124/125) = 124*5^y

5^x = 124*5^y*(125/124)


5^x = 5^y(125)

5^x = 5^y(5^3)

5^x = 5^y+3

x = y + 3

x - 3 = y

Answer: C


Could you help me understand the specific steps you took to get from the first bold line to the second? I'm not sure how you managed to get rid of the fraction here. Thanks!
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Re: If 5^x – 5^(x- 3) = 124*5^y, what is y in terms of x?  [#permalink]

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New post 06 Jun 2020, 03:49
travelwithbrandon wrote:
ScottTargetTestPrep wrote:
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



We can simplify the given equation:

5^x – 5^(x- 3) = 124*5^y

5^x – (5^x)(5^- 3) = 124*5^y

5^x(1 – (5^- 3)) = 124*5^y

5^x(1 – 1/125) = 124*5^y

5^x(1 – 1/125) = 124*5^y

5^x(124/125) = 124*5^y

5^x = 124*5^y*(125/124)


5^x = 5^y(125)

5^x = 5^y(5^3)

5^x = 5^y+3

x = y + 3

x - 3 = y

Answer: C


Could you help me understand the specific steps you took to get from the first bold line to the second? I'm not sure how you managed to get rid of the fraction here. Thanks!


Response:

Notice that in the first bold line, the fraction 124/125 is not in the exponent; that fraction is simply being multiplied by 5^x (as a matter of fact, nothing besides x is in the exponent on and after the third line). Thus, to get rid of the fraction 124/125 on the left hand side, I simply multiplied each side of the equation by 125/124.
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Re: If 5^x – 5^(x- 3) = 124*5^y, what is y in terms of x?   [#permalink] 06 Jun 2020, 03:49

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