Latest Elitmus Aptitude Question SOLUTION: if y>1 and x>=y then what is the maximum value of log [root x/y]base x + log[y/x]base y? a)-0.5 b)0 c)1 d)0.5

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(#M40039524) ELITMUS Numerical Ability question Keep an EYE

if y>1 and x>=y then what is the maximum value of log [root x/y]base x + log[y/x]base y?
a)-0.5
b)0
c)1
d)0.5

Asked In Elitmus asmit (9 years ago)

Unsolved Read Solution (14)

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Read Solution (14) :

Siddartha Mulumudi  (9 years ago)

Question should be log [root x/y]base x + log[root y/x]base y

log [root x/y]base x + log[root y/x]base y = 1/2(log [x/y]base x + log[y/x]base y)
= 1/2(log x(base x) - log y(base x) + log y(base y) - log x(base y))
=1/2(2- log y(base x) - log x(base y))
let k= log y(base x) => 1/k = log x(base y)

=1/2(1-[k+1/k]
as x,y>1 log x(base y) > 0, log y(base x) > 0 => k> 0
so K+1/k has a minimum value of 2.
Put it there it becomes 0. which is max value of the equation

0

Is this solution Helpfull? Yes (16) | No (3)  

nitin sehalot  (9 years ago)

ans should be 0.5

Is this solution Helpfull? Yes (11) | No (5)  

tauseef arbab  (9 years ago)

Answer will be 1
because solving the expression
last equation becomes 1-(1/2)[log y to the base x - log x to the base y]
put the value of y=2 and x=2
we get maximum value as 1

Is this solution Helpfull? Yes (8) | No (9)  

tauseef arbab  (9 years ago)

answer is 0.....
sorry for the wrong answer

Is this solution Helpfull? Yes (8) | No (1)  

Narasapu Hari prasad  (9 years ago)

ans is 0,zero
log[root x/y]base x+ log[x/y]base y
1/2(logx base x-logy base x)+logx base y-log y base y
put x=10,y=10
so 1/2(1-1)+1-1)=0

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amit kumar gupta  (9 years ago)

ans should be -0.5

Is this solution Helpfull? Yes (5) | No (1)  

shailesh verma  (9 years ago)

ans will be 1

Is this solution Helpfull? Yes (1) | No (3)  

Arvind Kumar  (9 years ago)

1/2[logx-logy/logx]+[logy-logx/logy]
1/2[1-logy/logx]+[1-logx/logy]
put x=y=2
1/2[1-1]+[1-1]=0
so,answer is 0.

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

ANANT VIKRAM SINGH  (9 years ago)

1/2+1/2[logy]-3/2[logx]....final expression with changing base also
put val x=y=10
answer is 0.5

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Amit Kumar Singh  (7 years ago)

solving the equation you will get 1/2[2-logx^y-logy^x]
to maximize this calculate the minimum value of these two by putting y=x
1/2[2-1-1]=0

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Siri  (9 years ago)

log(√x) base x - log y basex + log( y ^2) base y - log x base y
0.5 +2 -[ log y base x + log x base ] = 0.5+2-2 = 0.5
min value of x+ 1/x =2

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Kumar Vikash  (9 years ago)

.5 is the answer
becos if u take value of x>y then right part of expresion become undefind then left part give the value approxmatily equal to 0.5 and if u check x=y then it gives 0 .then max value is 0.5

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Rohit Dengre  (9 years ago)

0
(1/2)[log y to the base x - log x to the base y]
since x>=y
if we put x=y
ans.=0

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KAMESH TYAGI  (9 years ago)

=1/2logbasex (x/y) + logbasey (y/x)
=1/2[logbasex x - logbasex y] +logbasey y - logbasey x
=1/2[1 - logbasex y] + 1 - logbasey x
=3/2 -1/2 logbasex y - logbasey x
now let x=10 and y=10
=(3/2) - (3/2)
=0
So answer is 0

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