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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 --> \(n=21\).

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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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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