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21 Apr 2020, 09:06
Kudos
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B
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Difficulty:
65%
(hard)
Question Stats:
65% (02:55) correct
35%
(02:47)
wrong
based on 303
sessions
History
Date
Time
Result
Not Attempted Yet
If \(4^{(6 + 12 + 18 + 24 + … + 6x)} = (0.0625)^{(-84)}\), what is the value of x?
A. 6
B. 7
C. 8
D. 9
E. 12
Are You Up For the Challenge: 700 Level Questions
A. 6
B. 7
C. 8
D. 9
E. 12
Are You Up For the Challenge: 700 Level Questions
21 Apr 2020, 09:18
Kudos
Bookmarks
Bunuel
\(4^{(6 + 12 + 18 + 24 + … + 6x)} = (0.0625)^{(-84)}=(\frac{625}{10000})^{(-84)}=((\frac{5}{10})^4)^{-84}=((\frac{1}{2})^4)^{-84}=(2^4)^{84}=4^{2*84}\)
Equating the powers of 4 ..
\((6+12+...6x)=2*84..........6(1+2+3....+x)=2*84\).
\(1+2+...+x=2*14\).
\(\frac{x(x+1)}{2}=2*14\).
\(x(x+1)=2*2*14=2*2*2*2*7=7*8....x=7\)
B
02 Aug 2020, 11:03
Kudos
Bookmarks
[quote="Bunuel"]If \(4^{(6 + 12 + 18 + 24 + … + 6x)} = (0.0625)^{(-84)}\), what is the value of x?
A. 6
B. 7
C. 8
D. 9
E. 12
4^{(6 + 12 + 18 + 24 + … + 6x)} = (0.0625)^{(-84)
4^{(6 + 12 + 18 + 24 + … + 6x)} = (10000/625)^84=4^168
6 + 12 + 18 + 24 + … + 6x=168
6(1+2+3+4....+6x)=168
1+2+3....+x=28
x=7
B
A. 6
B. 7
C. 8
D. 9
E. 12
4^{(6 + 12 + 18 + 24 + … + 6x)} = (0.0625)^{(-84)
4^{(6 + 12 + 18 + 24 + … + 6x)} = (10000/625)^84=4^168
6 + 12 + 18 + 24 + … + 6x=168
6(1+2+3+4....+6x)=168
1+2+3....+x=28
x=7
B
