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Which of the following best approximates the value of q if \(5^{28}+3^{11}=5^q\) ?
A. 39
B. 30
C. 28
D. 27
E. 17
A. 39
B. 30
C. 28
D. 27
E. 17
01 Apr 2012, 23:51
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Smita04
Which of the following best approximates the value of q if 5^28 + 3^11 = 5^q ?
(A) 39
(B) 30
(C) 28
(D) 27
(E) 17
(A) 39
(B) 30
(C) 28
(D) 27
(E) 17
The answer has to be at least 28 since you are adding something to 5^28.
Note that 3^11 is much much smaller than 5^28 so adding it will not change the value of 5^28 much. If it is hard to visualize, think of it this way:
The next possible answer is 5^30 which is greater than 5^28
5^30 = 25*5^28
But
5^28 + 5^28 = 2*5^28
Even if we add 5^28 to 5^28, all we get is 2*5^28 which is much much smaller than 25*5^28
In fact, what we are actually adding is only 3^11 so 5^28 + 3^11 must be much closer to 5^28. Hence its value must be approximately 5^28.
23 Aug 2010, 10:12
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Question should read:
Which of the following best approximates the value of q if \(5^{28}+3^{11}=5^q\)?
A. 39
B. 30
C. 28
D. 27
E. 17
Note that we need approximate value of \(q\). Now, \(5^{28}\) is much, much, much bigger than \(3^{11}\). So adding \(3^{11}\) to \(5^{28}\) will be closer to \(5^{28}\) then to \(5^{29}\), basically \(3^{11}\) is negligible in this case. So \(q\approx{28}\).
Answer: C.
Which of the following best approximates the value of q if \(5^{28}+3^{11}=5^q\)?
A. 39
B. 30
C. 28
D. 27
E. 17
Note that we need approximate value of \(q\). Now, \(5^{28}\) is much, much, much bigger than \(3^{11}\). So adding \(3^{11}\) to \(5^{28}\) will be closer to \(5^{28}\) then to \(5^{29}\), basically \(3^{11}\) is negligible in this case. So \(q\approx{28}\).
Answer: C.
