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# Does 5^x=7^y?

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Senior SC Moderator
Joined: 14 Nov 2016
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08 Feb 2017, 01:28
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Difficulty:

95% (hard)

Question Stats:

38% (01:32) correct 63% (01:30) wrong based on 148 sessions

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Tricky Question.

Does $$5^x=7^y$$?

(1) $$x>y>0$$

(2) $$x$$ and $$y$$ are both even.

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08 Feb 2017, 04:54
1
5
ziyuenlau wrote:

Tricky Question.

Does $$5^x=7^y$$?

(1) $$x>y>0$$

(2) $$x$$ and $$y$$ are both even.

Hi

When can $$5^x=7^y$$?..
When x=y=0, both are EQUAL to 1..
Also for a certain non-integer value of x and y, both will be EQUAL..

Let's see the statements...

(1) $$x>y>0$$
X=y=0 is ruled out but still for a certain non-integer value of x and y, both will be EQUAL otherwise they will not be same..
Insufficient..

(2) $$x$$ and $$y$$ are both even.[/quote]
x=y=0, and is YES..
x=0, y=2, ans is NO..
Insufficient..

Combined..
Both are even and not ZERO, so ans will always be NO..
Sufficient
C
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21 Sep 2017, 09:31
chetan2u wrote:
ziyuenlau wrote:

Tricky Question.

Does $$5^x=7^y$$?

(1) $$x>y>0$$

(2) $$x$$ and $$y$$ are both even.

Hi

When can $$5^x=7^y$$?..
When x=y=0, both are EQUAL to 1..
Also for a certain non-integer value of x and y, both will be EQUAL..

Let's see the statements...

(1) $$x>y>0$$
X=y=0 is ruled out but still for a certain non-integer value of x and y, both will be EQUAL otherwise they will not be same..
Insufficient..

(2) $$x$$ and $$y$$ are both even.

x=y=0, and is YES..
x=0, y=2, ans is NO..
Insufficient..

Combined..
Both are even and not ZERO, so ans will always be NO..
Sufficient
C[/quote]

Hello Chetan,

Could you please explain on this

Also for a certain non-integer value of x and y, both will be EQUAL..
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28 Mar 2018, 05:36
But how do we know that apart from 0 if there is/are another value which satisfies the equation is even or not. If one pair is even, then answer will be C, but if more than one, it might be E. How can we conclude in this way without knowing other possible values of x and y ??

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28 Mar 2018, 06:48
SonalSinha803 wrote:
But how do we know that apart from 0 if there is/are another value which satisfies the equation is even or not. If one pair is even, then answer will be C, but if more than one, it might be E. How can we conclude in this way without knowing other possible values of x and y ??

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Hi..
If x and y are integer..
5^x will have only 1 and 5 as factor and 7^y will have 1 and 7 as factor..
So they both cannot be equal ever..
Only possiblity is if both are 1 when x and y are 0..
Also there is always some non integer value where 5°x could be 7..
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28 Mar 2018, 08:00
Chetan2u... can you please elaborate which all non integer values are available wherein 5^x equals 7... as if as a layman I solve question then I would have marked A without knowing the values of non integers.

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28 Mar 2018, 08:11
why is it not A? Since, x and y are greater than 0, 5 to any power cannot be equal to 7 to any power.
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28 Mar 2018, 21:24
chetan2u wrote:
SonalSinha803 wrote:
But how do we know that apart from 0 if there is/are another value which satisfies the equation is even or not. If one pair is even, then answer will be C, but if more than one, it might be E. How can we conclude in this way without knowing other possible values of x and y ??

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Hi..
If x and y are integer..
5^x will have only 1 and 5 as factor and 7^y will have 1 and 7 as factor..
So they both cannot be equal ever..
Only possiblity is if both are 1 when x and y are 0..
Also there is always some non integer value where 5°x could be 7..

Okay got it.....and now I know decimals cannot be even or odd....this is where I was confused.... thankyou so much ?

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28 Mar 2018, 23:26
lilyb wrote:
why is it not A? Since, x and y are greater than 0, 5 to any power cannot be equal to 7 to any power.

There is always some NON integer (decimal) value for which the entities will be equal. If you want to know this for sure. Apply logarithm to both sides of equation. After applying look into the log table for log 5 and log 7. And for some certain value the product on both the values will be equal.

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28 Mar 2018, 23:27
chetan2u wrote:
ziyuenlau wrote:

Tricky Question.

Does $$5^x=7^y$$?

(1) $$x>y>0$$

(2) $$x$$ and $$y$$ are both even.

Hi

When can $$5^x=7^y$$?..
When x=y=0, both are EQUAL to 1..
Also for a certain non-integer value of x and y, both will be EQUAL..

Let's see the statements...

(1) $$x>y>0$$
X=y=0 is ruled out but still for a certain non-integer value of x and y, both will be EQUAL otherwise they will not be same..
Insufficient..

(2) $$x$$ and $$y$$ are both even.

x=y=0, and is YES..
x=0, y=2, ans is NO..
Insufficient..

Combined..
Both are even and not ZERO, so ans will always be NO..
Sufficient
C[/quote]
The best point chetan2u does not fail to consider like the rest is x and y in statement 1 can be non integers.

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Re: Does 5^x=7^y?   [#permalink] 28 Mar 2018, 23:27
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