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Difficulty:
5%
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Question Stats:
89% (00:58) correct
11%
(01:42)
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based on 1360
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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
A. 11
B. 21
C. 22
D. 23
E. 32
09 Aug 2010, 03:36
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Yalephd
If 5^21 X 4^11 = 2x10^n. What is the value of n?
A. 11
B. 21
C. 22
D. 23
E. 32
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 --> \(n=21\).
Answer: B.
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
Answer: 21 (B)
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
Answer: 21 (B)
