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# If 5^21 * 4^11 = 2 * 10^n, what is the value of n?

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If 5^21 * 4^11 = 2 * 10^n, what is the value of n? [#permalink]

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08 Aug 2010, 21:12
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If $$5^{21} * 4^{11} = 2 * 10^n$$, what is the value of n?

A. 11
B. 21
C. 22
D. 23
E. 32
[Reveal] Spoiler: OA

Last edited by Bunuel on 04 Oct 2017, 06:39, edited 4 times in total.
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Re: If 5^21 * 4^11 = 2 * 10^n, what is the value of n? [#permalink]

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08 Aug 2010, 21:41
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My attempt:

5^(21) * 4^(11) = 2*10^p

5^(21) * 2 ^ (22) = 2 * (2*5)^p

5^(21) * 2 ^ (22) = 2 * 2^(p) * 5^(p)

5^(21) * 2 ^ (22) = 2^(p+1) * 5^(p)

=> (p+1) = 22

=> p = 21

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Re: If 5^21 * 4^11 = 2 * 10^n, what is the value of n? [#permalink]

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09 Aug 2010, 03:36
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Yalephd wrote:
If 5^21 X 4^11 = 2x10^n. What is the value of n?

A. 11
B. 21
C. 22
D. 23
E. 32

When we have exponents on both sides it's good idea to get common base.

We have $$5^{21}*4^{11}=2*10^n$$. Little trick for this question: we can forget about 2's on both sides and concentrate on 5-s --> $$5^{21}*4^{11}=2*2^n*5^n$$ --> powers of 5 on both sides must be equal --> $$n=21$$.

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Re: If 5^21 * 4^11 = 2 * 10^n, what is the value of n? [#permalink]

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09 Aug 2010, 04:57
I got it now using ezhilkumarank's method. Thanks.
Bunuel, I don't follow your method. Are you saying that 5^21 * 4^11 = 2 * 2^21 * 5^21

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Re: If 5^21 * 4^11 = 2 * 10^n, what is the value of n? [#permalink]

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09 Aug 2010, 06:15
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Yalephd,

What Bunuel is trying to say is that save time by considering only 5

We have 10^p = (2*5)^p = 2^p * 5^p

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Re: If 5^21 * 4^11 = 2 * 10^n, what is the value of n? [#permalink]

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14 Aug 2010, 16:12
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vasili wrote:
Can somebody please put detailed explanation? Thanks.

If 5^21 x 4^11=2x10^n, what's n?

11
21
22
23
32

@ vasili
-- This question is already answered in one of the earlier post. Kindly search for the question once before posting.

5^21 * 4^11=2*10^n

= 5^21 * 4^11=2*(2*5)^n

= 5^21 * 4^11 = 2^(n+1) * 5^n

=> n = 21.
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Re: If 5^21 * 4^11 = 2 * 10^n, what is the value of n? [#permalink]

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23 Aug 2010, 09:27
I know there is an easy way to solve this quickly, but I am wondering if someone can explain it:

5^21 x 4 ^11 = 2 x 10 ^ n

What is n?

Thank you very much.

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Re: If 5^21 * 4^11 = 2 * 10^n, what is the value of n? [#permalink]

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23 Aug 2010, 09:36
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5^21 2^22 = 2 10^n
10^21 = 10^n
Hence n = 21

Posted from my mobile device
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Re: If 5^21 * 4^11 = 2 * 10^n, what is the value of n? [#permalink]

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26 Aug 2010, 19:08
I have a weird mind block around this question....
what is the value of n if,
5^21 x 4^11 = 2 x 10^n

Ugh, it seems like it should be so easy! what am I not getting? Thanks so much in advance for anyone who can shine some light onto this!

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Re: If 5^21 * 4^11 = 2 * 10^n, what is the value of n? [#permalink]

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26 Aug 2010, 19:10
kaptnmorgz wrote:
I have a weird mind block around this question....
what is the value of n if,
5^21 x 4^11 = 2 x 10^n

Ugh, it seems like it should be so easy! what am I not getting? Thanks so much in advance for anyone who can shine some light onto this!

This is easy. Just try to isolate the powers of the distinct primes and then solve for x.

P.S: This question is already discussed earlier. You may search for the answer once after trying again.
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Re: If 5^21 * 4^11 = 2 * 10^n, what is the value of n? [#permalink]

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26 Aug 2010, 23:07
simplification is -

5^21 * 2^22 = 2 * 2^n * 5^n
= 2^(n+1) * 5^n

comparing L.H.S and R.H.S, n = 21

Thanks.

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Re: If 5^21 * 4^11 = 2 * 10^n, what is the value of n? [#permalink]

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04 Aug 2013, 11:31
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njkhokh wrote:
If 5^21 x 4^11 = 2 x 10^n what is the value of n?

A) 11
B) 21
C) 22
D) 23
E) 32

$$5^21$$$$*4^11$$ $$= 2*10^n$$

$$5^21* 2^22 = 2 *10^n$$ ( AS $$4^11= (2^2)^11$$)

$$(5.2)^21 * 2 = 2 * 10^n$$

HENCE n = 21
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Last edited by blueseas on 04 Aug 2013, 11:36, edited 1 time in total.

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Re: If 5^21 * 4^11 = 2 * 10^n, what is the value of n? [#permalink]

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04 Aug 2013, 11:36
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njkhokh wrote:
If 5^21 x 4^11 = 2 x 10^n what is the value of n?
A) 11
B) 21
C) 22
D) 23
E) 32

5^21 x 4^11 = 2 x 10^n
5^21 x 2^22 = 2 x 10^n
2 x 5^21 x 2^21 = 2 x 10^n
2 x 10^21 = 2 x 10^n

Thus n = 21
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Re: If 5^21 * 4^11 = 2 * 10^n, what is the value of n? [#permalink]

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26 Feb 2014, 21:58
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$$5^{21} * 4^{11} = 2*10^p$$

$$5^{21} * 2^{22} = 2*10^p$$

$$2 * 2^{21} * 5^{21} = 2*10^p$$

$$2 * 10^{21} = 2*10^p$$

Equating powers, p = 21 = Answer B
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Last edited by PareshGmat on 15 Apr 2014, 01:56, edited 1 time in total.

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Re: If 5^21 * 4^11 = 2 * 10^n, what is the value of n? [#permalink]

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14 Apr 2014, 18:23
hi, all!

quick exponent question which seems easy but i cant seem to get my head around it - reallly appreciate your help!!

If 5^21 x 4^11 = 2 x 10^n,, what is value of n?

answer is 21, but honestly cant remember quite how to get here - thanks again for any help!

Thumb rule for any exponents question: Deal only in prime numbers.

$$5^{21} * 4^{11} = 2 * 10^n$$

$$5^{21} * 2^{22} = 2 * 2^n * 5^n$$

$$5^{21} * 2^{22} = 2^{n+1} * 5^n$$

Now match the exponents of same prime numbers. Power of 5 on both sides should be equal.
21 = n
or
Power of 2 on both sides should be equal.
22 = n+1
n = 21
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Re: If 5^21 * 4^11 = 2 * 10^n, what is the value of n? [#permalink]

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27 Aug 2016, 23:53
SharmaShruti wrote:
5^21 X 4^11 = 2 X 10^n. What is the value of n?
a) 11
b) 21
c) 22
d) 23
e)32

The given expression $$5^21 * 4^(11) = 2 * 10^n$$ can be written as $$5^21 * 2^22 = 2 * 5^n * 2^n$$

or $$5^21 * 2^22 = 5^n * 2^(n+1)$$

Comparing the powers of 2 on both sides, we will have $$2^22 = * 2^(n+1)$$

or 22=n+1 or n=21. hence B
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Re: If 5^21 * 4^11 = 2 * 10^n, what is the value of n? [#permalink]

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28 Aug 2016, 06:38
SharmaShruti wrote:
5^21 X 4^11 = 2 X 10^n. What is the value of n?
a) 11
b) 21
c) 22
d) 23
e)32

Hi,
One does not require to simplify anything..
On left hand side, the power of 5 is 21.....
But on right side it is part of 10.. so power of 10 has to be same as that of 5..
Ans 21
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Re: If 5^21 * 4^11 = 2 * 10^n, what is the value of n? [#permalink]

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Re: If 5^21 * 4^11 = 2 * 10^n, what is the value of n? [#permalink]

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06 Oct 2017, 10:53
Yalephd wrote:
If $$5^{21} * 4^{11} = 2 * 10^n$$, what is the value of n?

A. 11
B. 21
C. 22
D. 23
E. 32

We can simplify the given equation:

5^21 x 2^22 = 2^1 x 10^n

5^21 x 2^21 = 10^n

10^21 = 10^n

21 = n

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Re: If 5^21 * 4^11 = 2 * 10^n, what is the value of n?   [#permalink] 06 Oct 2017, 10:53
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