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What is y in terms of x ?

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New post 08 May 2018, 15:54
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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
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Re: What is y in terms of x ?  [#permalink]

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New post 08 May 2018, 16:15
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FillFM 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)\((5^y)\)
or \(5^x\) – \(\frac{5^x}{5^3}\) = \((125-1)\)\((5^y)\)
or \(\frac{(5^x*5^3-5^x)}{5^3}\) = \((5^3-1)\)\((5^y)\)
or \(5^x*(5^3-1)\) = \((5^3-1)\)\((5^y)(5^3)\)
or \(5^x\) = 5^(y+3)
==> \(x=y+3\)
==>\(y=x-3\) ..................Thus the answer is option C.
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Re: What is y in terms of x ?  [#permalink]

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New post 08 May 2018, 18:58
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FillFM 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)\((5^y)\)
\(5^x\) * (1 - 5^-3) = (124)\((5^y)\) ---- Take out \(5^x\) common.
\(5^x\) * \(\frac{(125 - 1)}{125}\) = (124)\((5^y)\)
\(5^x\) * \(\frac{124}{125}\) = (124)\((5^y)\)
\(5^x\) * \(\frac{1}{125}\) = \((5^y)\) --- Striking out 124.
\(5^x\) = 5^(y+3)

x=y+3 -> y= x- 3

Answer: (C).
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Re: What is y in terms of x ?  [#permalink]

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New post 08 May 2018, 19:39
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FillFM wrote:
If \(5^x\) – 5^(x–3) = (124)\((5^y)\), what is y in terms of x ?


The shortest way is to substitute a real number for x. Let's say x =3, then \(5^3\) – 5^(3–3) = (124)\((5^y)\)
and it gives us that y = 0

A) x = 3
B) x – 6 = 3-6=-3
C) x – 3 = 0 - correct
D) 2x + 3 = 9
E) 2x + 6 = 12

Answer (C)
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Re: What is y in terms of x ?  [#permalink]

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New post 29 May 2018, 12:50
seed wrote:
FillFM 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)\((5^y)\)
\(5^x\) * (1 - 5^-3) = (124)\((5^y)\) ---- Take out \(5^x\) common.
\(5^x\) * \(\frac{(125 - 1)}{125}\) = (124)\((5^y)\)
\(5^x\) * \(\frac{124}{125}\) = (124)\((5^y)\)
\(5^x\) * \(\frac{1}{125}\) = \((5^y)\) --- Striking out 124.
\(5^x\) = 5^(y+3)

x=y+3 -> y= x- 3

Answer: (C).



Hi pushpitkc

cab you expain based on which rule do we take out \(5^x\) common

i mean if it were like this (2x+7x) i understand we take out common x --> x(2+7)

but in this case \(5^x\) – \(5^{x-3}\) = \((124)\)\((5^y)\) how can we take common \(5^x\) it is not even in the brackets and there is only only one \(5^x\) :?

Also how after this \(5^x\) * \(\frac{1}{125}\) = \((5^y)\) --- Striking out 124.

we get this \(5^x\) = 5^(y+3) :?

thanks for your great help :)
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New post 29 May 2018, 13:36
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dave13 wrote:

Hi pushpitkc

cab you expain based on which rule do we take out \(5^x\) common

i mean if it were like this (2x+7x) i understand we take out common x --> x(2+7)

but in this case \(5^x\) – \(5^{x-3}\) = \((124)\)\((5^y)\) how can we take common \(5^x\) it is not even in the brackets and there is only only one \(5^x\) :?

Also how after this \(5^x\) * \(\frac{1}{125}\) = \((5^y)\) --- Striking out 124.

we get this \(5^x\) = 5^(y+3) :?

thanks for your great help :)


Hey dave13

The first step is to understand what happens to \(5^{x-3}\).

\(5^{x+(-3)} = 5^{x}*5^{-3} = 5^{x}*\frac{1}{5^3} = 5^{x}*\frac{1}{125}\)

Now, \(5^x - 5^{x-3}\) = \(5^x – 5^{x}*\frac{1}{125}\) = \(5^x(1 - \frac{1}{125}) = \frac{124}{125} * 5^x\)

Now, since we have \(124\) on both sides, we will finally get \(5^x = 5^y*125 = 5^y*5^3 = 5^{y+3}\)

Hope this helps you.
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Re: What is y in terms of x ?  [#permalink]

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New post 14 Jul 2018, 19:13
FillFM 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)

We see that 5^(x - 3) is common to both terms on the left side of the equation, so we factor it out:

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

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

5^(x - 3) = 5^y

Recall that when the bases are equal, we can equate the exponents:

x - 3 = y

Answer: C
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Re: What is y in terms of x ?   [#permalink] 14 Jul 2018, 19:13
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