Latest Elitmus Aptitude Question SOLUTION: how many possible solution for (log a +log b +log c)/(log 6)= 6? ( take log to the base 10)

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(#M40155459) ELITMUS Numerical Ability question quant Keep an EYE

how many possible solution for (log a +log b
+log c)/(log 6)= 6? ( take log to the base 10)

Asked In Elitmus prince kumar (8 years ago)

Unsolved Read Solution (4)

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Read Solution (4) :

Mukesh Kumar Singh  (8 years ago)

log a + log b +log c = log abc
we need to find log abc/log 6
=> log (base6)abc = 6
=> 6^6 = abc
=>3x3x3x3x3x3x2x2x2x2x2x2x1 = abc
now its a combination problem
'a' can be chosen in 7x7 ways
i.e (0 threes or 1 three or 2 threes ....or 6 threes)AND(0 two or 1 two or 2 twos... 6 twos)
then after 'b' can be chosen in (7x7)-1 [ ie same thing that is chosen as 'a' cannot be chosen as 'b']
when 'a' and 'b' are chosen 'c' can only be one thing [i.e all remaining numbers multiplied]
so its 49x48 ways = 2352

Is this solution Helpfull? Yes (9) | No (7)  

Ankur  (8 years ago)

question was how many possible solutions for (log a +log b
+log c)/(log 6)= 6? If abc are in G.P

soln :- log abc / (log 6)= 6

take a = a
b= ar
c= ar^2
then log base 6 abc = 6
abc =6^6
then (ar)^3=6^6
ar=36
ar= 2^2 * 3^2
factors of 36 will be 9

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ashutosh mishra  (7 years ago)

log6(abc)=6
log6abc=log666
abc=6^6
possible cases=
a=6^6 b=1 c=1 3 soln
a=6^5 b=6 c=1 3 soln
a=6^4 b=6^2 c=1 3 soln
a=6^4 b=6 c=6 3 soln
a=6^3 b=6^3 c=1 3 soln
a=6^3 b=6^2 c=1 3 soln
a=6^2 b=6^2 c=6^2 1 soln
total 19 soln

Is this solution Helpfull? Yes (2) | No (1)  

Pawan Kumar Shukla  (7 years ago)

log(A*B*C) = 6*log 6 then log(A*B*C) = log(6^6)

so A*B*C = 6*6*6*6*6*6
so no of possibilities are
(6*6,6*6,6*6) = 1
(6*6*6,6*6,6) = 6
(6*6*6*6,6,6) = 3
so total 10 ways i think

Is this solution Helpfull? Yes (1) | No (1)  

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