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

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yashikaaggarwal
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If 5^x – 5^(x- 3) = 124*5^y, what is y in terms of x? [#permalink] New post   22 Aug 2020, 06:44
Genoa2000 wrote:
What level is this question? Where can I see the level of the questions?

Not always I find it... :?

Its mentioned in the left hand corner just before the question starts. sub 600
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Preeeeeetika
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Re: If 5^x – 5^(x- 3) = 124*5^y, what is y in terms of x? [#permalink] New post   04 Feb 2022, 09:00
Question: If 5^x – 5^(x- 3) = 124*5^y, what is y in terms of x?

Pre- analysis
1. Notice that 124 is 1 less than 125, i.e - 5^3
2. On the LHS you have 5^x – 5^(x- 3)

Working from the LHS
5^3 gives us 125, we need to subtract this by 1 to get 124
hence, we would need 5^(x- 3) to equal 1. This can only happen if 5^0 and x = 3

Hence, our LHS becomes: 5^3 - 5^(3-3)

Same thing on the RHS
We need to keep 124, and this can be done by multiplying it with 1. This can only happen if 5^0

Finally we have: 5^3 - 5^(3-3) = 124 * 5^0
5^3 - 5^0 = 124 * 5^0
125-1 = 124*1
124=124

Hence: x=3, y=0
and y= x-3

I hope this helps those weak in quants (like myself)!
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If 5^x 5^(x- 3) = 124*5^y, what is y in terms of x? [#permalink] New post   19 Nov 2022, 14:23
Bunuel 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

\(5^x-5^{x-3}=124*5^y\);

Factor out \(5^{x-3}\) to get \(5^{x-3}(5^3-1)=124*5^y\);

\(5^{x-3}=5^y\);

Bases are equal so we can equate the powers: \(y=x-3\).

Answer: C.


Bunuel
Why can't 5^x - 5^(x-3) be converted to 5^3? ---> if you subtract the exponents, x-x+3=3

Both terms have the same base of 5, so why can't the exponents simply be subtracted here? Thank you!
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sanebeyondone
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If 5^x 5^(x- 3) = 124*5^y, what is y in terms of x? [#permalink] New post   22 Nov 2023, 01:46
PareshGmat wrote:
\(5^x – 5^{(x- 3)} = 124*5^y\)

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


Hi PareshGmat,
I don't understand how equating the powers in the last part makes y = x+3. Could you please kindly explain.

Edit: i just noticed. think you wrote it wrong the answer should be y= x-3 not y = x+1
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If 5^x 5^(x- 3) = 124*5^y, what is y in terms of x? [#permalink]
22 Nov 2023, 01:46
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