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If 3^a * 4^b = c, what is the value of b? (1) 5^a = 25 (2) c

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If 3^a * 4^b = c, what is the value of b? (1) 5^a = 25 (2) c [#permalink] New post 01 May 2011, 06:42
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If 3^a * 4^b = c, what is the value of b?

(1) 5^a = 25
(2) c = 36
[Reveal] Spoiler: OA

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Re: what is the value of b? [#permalink] New post 02 May 2011, 03:45
straight B. 36 = 2 ^2 * 3^2
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Re: what is the value of b? [#permalink] New post 09 Nov 2011, 07:52
I'm going to go with B

36 = \(3^2 and 2^2\)

you are given that \(3^a*4^b=c\)

we can break down 4 to 2^2b
So now we have

\(3^a*2^2b=2^2*3^2\)

so a= 2, b = 2
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Re: what is the value of b? [#permalink] New post 09 Nov 2011, 08:41
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a and b are not integers here.

consider this:

Now for every value of a, there is a different value of b.
Say, a = 1, then 4^b = 12 and b = 1.79 approx
a = 2, then 4^b = 4 and b = 1
a = 3, then 4^b = 36/27 and b = 0.2 approx

so answer is C
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Re: If 3^a * 4^b = c, what is the value of b? (1) 5^a = 25 (2) c [#permalink] New post 13 Nov 2011, 08:20
The question does not mention a and b to be Integers.
Individually,none of the statements suffice to reach the value of b.

Both the statements when used together,give the value of b.
3^2 * 4^b = 36.
b=1

Hence C.
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Re: what is the value of b? [#permalink] New post 04 Feb 2012, 14:50
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amit2k9 wrote:
straight B. 36 = 2 ^2 * 3^2


If 3^a*4^b = c, what is the value of b?

Note that we are not told that the variables are integers only.

(1) 5^a = 25 --> \(a=2\), but we can not get the values of \(b\). Not sufficient.

(2) c = 36 --> \(3^a*4^b = c\): it's tempting to write \(3^2*4^1=36\) and say that \(b=1\) but again we are not told that the variables are integers only. So, for example it can be that \(3^a=36\) for some non-integer \(a\) and \(b=0\), making \(4^b\) equal to 1 --> \(3^a*4^b =36*1=36\). Not sufficient.

(1)+(2) As \(a=2\) and \(c = 36\) then \(9*4^b=36\) --> \(b=1\). Sufficient.

Answer: C.

Hope it's clear.
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Re: If 3^a * 4^b = c, what is the value of b? (1) 5^a = 25 (2) c [#permalink] New post 30 Sep 2014, 22:42
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Re: If 3^a * 4^b = c, what is the value of b? (1) 5^a = 25 (2) c [#permalink] New post 19 Jun 2015, 07:15
Hi Bunnel in the above explantion how can 3^a=36 be possible for any value a, it has to have an even no. plz clarify my doubt
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Re: If 3^a * 4^b = c, what is the value of b? (1) 5^a = 25 (2) c [#permalink] New post 19 Jun 2015, 07:21
Expert's post
caster88 wrote:
Hi Bunnel in the above explantion how can 3^a=36 be possible for any value a, it has to have an even no. plz clarify my doubt


We are NOT told that a and b are integers. So, there exists some irrational a for which 3^a = 36: \(a= \frac{2 (log(2)+log(3))}{log(3)}\approx{3.2619}\)
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Re: If 3^a * 4^b = c, what is the value of b? (1) 5^a = 25 (2) c   [#permalink] 19 Jun 2015, 07:21
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