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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

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.

Re: If 3^a * 4^b = c, what is the value of b? (1) 5^a = 25 (2) c [#permalink]

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30 Sep 2014, 23:42

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Re: If 3^a * 4^b = c, what is the value of b? (1) 5^a = 25 (2) c [#permalink]

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19 Jun 2015, 08:21

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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