Latest Elitmus Aptitude Question SOLUTION: how many solution for x.... 1/2(log6(x^2-8x+16)+1/2(log6(x^2-9x+81)=1 a)0 b)1 c)3 d)4

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(#M40037884) ELITMUS Numerical Ability question logorithm Keep an EYE

how many solution for x....
1/2(log6(x^2-8x+16)+1/2(log6(x^2-9x+81)=1

a)0
b)1
c)3
d)4

Asked In Elitmus randeep kumar (9 years ago)

Unsolved Read Solution (10)

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Read Solution (10) :

soubhik mukherjee  (9 years ago)

>>log6((x-4)(x-9))=1.....(i)
>>log6((x-4)(x-9))=log6(6)
>>(x-4)(x-9)=6
by solving..x=3,10
eqn (i) is true for x=10, not for x=3
because, log(ab)=log(a)+log(b)
so, only 1 solution for x=10.
ans-b

Is this solution Helpfull? Yes (23) | No (4)  

ak  (9 years ago)

and
in place of 9x ,it was 18x

Is this solution Helpfull? Yes (12) | No (1)  

ak  (9 years ago)

1/2(log6(x^2-8x+16)+1/2(log6(x^2-9x+81)=1
1/2(log6(x^2-8x+16)+(log6(x^2-9x+81)))=1 , takng 1/2 common
log6(x^2-8x+16)+log6(x^2-9x+81)=2
log6((x^2-8x+16)(x^2-9x+81))=2 , acc to log rule log a + log b = log(a+b)
log6((x-4)^2(x-9)^2)=2
log6((x-4)(x-9))^2=2
2log6((x-4)(x-9))=2
log6((x-4)(x-9)) = 1
(x-4)(x-9)=6
x^2-13x+36 = 6
x = 3,10
so, there are two solns....

Is this solution Helpfull? Yes (10) | No (19)  

dheeraj  (9 years ago)

in place of 9x ,it was 18x.
by solving both the eq,we will get

log6((x-4)(x-9))=1
value of x will be 3

it will have only 1 solution

Is this solution Helpfull? Yes (8) | No (3)  

Pratik Mishra  (9 years ago)

1/2(Log6(x^2-8x+16))+1/2(Log6(X^2-9x+81))=1
1/2(Log6(x-4)^2)+1/2(Log6(x-9)^2)=1
log6((x-4)^2*(x-9)^2))=2log6(6)
so,
((x-4)^2)((x-9)^2)=6^2
either (x-4)^2=36 or (x-9)^2=36
if:(x-4)^2=36
x-4=+6 or x-4=-6
so, x=10 or x=-2
if:(x-9)^2=36
x-9=+6 or x-9=-6
so, x=15 or x= 3
number of solution is:4

Is this solution Helpfull? Yes (6) | No (10)  

ak  (9 years ago)

log rule was (log a + log b) = log(a*b)

Is this solution Helpfull? Yes (3) | No   

anan kumar  (9 years ago)

if u hv sm common sense thn don't wrt wrng qstns

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LOKESH RANJAN  (9 years ago)

b,loga+logb=logab

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PRATIM JANA  (8 years ago)

there is no solution for this q . so ans is a) zero

Is this solution Helpfull? Yes | No (1)  

Manisha Choudhary  (7 years ago)

Ans is b.
It satisfy for only 10 not for 3.
As, log6((x-4)(x-9))=log6(6)
Put x = 10 in above equation
log 6 base 6 = log 6 base 6
Hence proved. ;)

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