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# What is y in terms of x ?

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Manager
Joined: 22 Jun 2017
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What is y in terms of x ?  [#permalink]

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08 May 2018, 15:54
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Question Stats:

81% (00:52) correct 19% (00:46) wrong based on 67 sessions

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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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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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08 May 2018, 18:58
1
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

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Re: What is y in terms of x ?  [#permalink]

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08 May 2018, 19:39
1
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

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Re: What is y in terms of x ?  [#permalink]

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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

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)

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What is y in terms of x ?  [#permalink]

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29 May 2018, 13:36
1
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)

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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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

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