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Re: Any short-cut way to solve this problem? [#permalink]
Carcass wrote:
223x=232×54

Originally posted by huda on 24 Jun 2019, 04:27.
Last edited by huda on 24 Jun 2019, 05:10, edited 3 times in total.
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Re: Any short-cut way to solve this problem? [#permalink]
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Sorry. I was editing the post. It was not completed.

See now :)
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Re: Any short-cut way to solve this problem? [#permalink]
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Hi,

which step you didnt get ??
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Re: Any short-cut way to solve this problem? [#permalink]
Carcass wrote:
Hi,

which step you didnt get ??


4th line RHS. How did you get 5th line RHS from 4th line RHS?
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Re: Any short-cut way to solve this problem? [#permalink]
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it is an exponent tule

26x26

Same base, then you can subtract the exponents

26x6
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Re: Any short-cut way to solve this problem? [#permalink]
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Carcass wrote:
223x=232×54


shouldnt the x next to the 2 on the LHS?

Because the way I am reading the first line, is 2 to the power of 2 to the power of 3 x, and when you power it.

it would be 2 to the power of 8 to the power of x?


I dont understand why the x was carried over to the higher power than brought down?
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Re: If 2^8x=640000 [#permalink]
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It is not brought down.

it is a number raised to the power and this raised to the power.

it is 2 raised to the two and the latter raised to 3x

223x

Then you multiply the exponents and the result is 26x
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Re: Any short-cut way to solve this problem? [#permalink]
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Carcass wrote:
223x=232×54

26x=26×54



I guess, I dont know where the 8 went?

In the answer above, is the LHS or the RHS the 28x=640000?


edit:
In the problem, it is 8x, and x is multiplied by 8. I understand that 28 is like saying 223. I am having a hard time getting why the x is next to the three, not the second two.


I also understand if the {2^{{(2x)}^{3}}, then the x will be cubed

Originally posted by h8gre on 24 Jun 2019, 16:29.
Last edited by h8gre on 24 Jun 2019, 16:45, edited 1 time in total.
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Re: Any short-cut way to solve this problem? [#permalink]
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Carcass wrote:
223x=232×54

26x=26×54

26x6=54

26x623=5423

On the LHS simplified we do have the form we are looking for

22x2=54

Only A fits the RHS

More than this is impossible. manipulation and a touch of educating guess


I mean,
How did you get this 54 from this 5423?
or from 26x623=5423 to 22x2=54? Need overall explanation because it not easy for me to understand.
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Re: If 2^8x=640000 [#permalink]
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Yes you are right. I made a mistake to think it was raised to x and not multiplied by x

Ok attack from another perspective

1) 28x=26×104

2) 28x=2624×54

OR

28x28=28×22×5428

28x8=22×54

Now clearly all the exponents can be divided by four

22x2=212×5

22x2=52
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Re: If 2^8x=640000 [#permalink]
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Carcass wrote:
Yes you are right. I made a mistake to think it was raised to x and not multiplied by x

Ok attack from another perspective

1) 28x=26×104

2) 28x=2624×54

OR

28x28=28×22×5428

28x8=22×54

Now clearly all the exponents can be divided by four

22x2=212×5

22x2=52


Fully understand, Thanks. :) :thanks :gl :done
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Re: If 2^8x=640000 [#permalink]
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Carcass wrote:

28x8=22×54

Now clearly all the exponents can be divided by four

22x2=212×5

22x2=52



Can we divide the exponents by 4 irrespective of the base number?

Please can you provide an explanation. ( I have never came acrossed this rule :? )
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Re: If 2^8x=640000 [#permalink]
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pranab01 wrote:
Carcass wrote:

28x8=22×54

Now clearly all the exponents can be divided by four

22x2=212×5

22x2=52



Can we divide the exponents by 4 irrespective of the base number?

Please can you provide an explanation. ( I have never came acrossed this rule :? )


Exactly. That was my question too.

The final equation stands like this..
28x10=54
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Re: If 2^8x=640000 [#permalink]
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First of all the exponent is 8x-8 and not 8x-10

Secondly, I went down without some obvious step but indeed yes.

It is a simplification/manipulation.

regards
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Re: If 2^8x=640000 [#permalink]
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I had been waiting for you Sir and your insight.

Thank you
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Re: If 2^8x=640000 [#permalink]
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Carcass wrote:
First of all the exponent is 8x-8 and not 8x-10

Secondly, I went down without some obvious step but indeed yes.

It is a simplification/manipulation.

regards


Got that,

Just trying out to simplify

28x=640000

or 28x=262454=21054 ( 640000 = we know, 2^6 = 64 and now there are 4 zeros after 64, that means it will compiled with = 2^4 * 5^4 , since 2*5 =10)

Now taking square root on both sides

24x=2552

Dividing by 24on both sides

24x24=255224

24x24=252

Taking square root again,

22x22=52

or 22x2=52
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Re: If 2^8x=640000 [#permalink]
Carcass wrote:
First of all the exponent is 8x-8 and not 8x-10

Secondly, I went down without some obvious step but indeed yes.

It is a simplification/manipulation.

regards


Dude. I am just quoting what you said before.

Now clearly all the exponents can be divided by four


28x8=2254

Dividing by 4 will give you

28x10=54

Am I missing anything? :shock:

Originally posted by harishsridharan on 25 Jun 2019, 07:01.
Last edited by harishsridharan on 25 Jun 2019, 07:05, edited 1 time in total.
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