Latest NTSE Aptitude Question SOLUTION: If 2^x=8^(y + 1) & 9^y = 3^(x – 9) Find y

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(#M40009532) NTSE question Keep an EYE

If 2^x=8^(y + 1)
& 9^y = 3^(x – 9)
Find y

Asked In NTSE Devendra Marghade (12 years ago)

Solved Aman Read Solution (4)

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Read Solution (4) :

Aman  (12 years ago)

2^x=8^(y + 1)

or 2^x = (2^3)^(y+1) = 2^(3y+3) ... Bases are equal, powers must be equal.
so x= 3y+3 ....... (1)

& 9^y = 3^(x - 9)
(3^2)^y = 3^(x-9)
3^2y = 3^(x-9).... bases are equal. so powers must also be equal.
2y = x-9 ......... (2)

From (1) and (2)
2y = 3y+3-9= 3y-6
y=6
and hence
x= 21.

Is this solution Helpfull? Yes (7) | No (1)  

Vignesh  (12 years ago)

Y = 6

Question :
If 2^x = 8^(y + 1) & 9^y = 3^(x - 9). Find y

Answer :

2^x = 8^(y + 1) ---->(1)
9^y = 3^(x - 9) ---->(2)

Put Y=6 in condition(1)
2^x = 8^(6+1)
2^x = 8^7
2^x = 2097152

2^21 = 2097152. (So, x=21).

Apply x=21 value in Condition(2)
9^y = 3^(x-9)
9^y = 3^(21-9)
9^y = 3^(12)
9^y = 531441

9^6 = 531441 (Y=6; X=21)
Conditions Satisfy.

So, Y=6; X=21;

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Jeevan  (12 years ago)

y=6

Well explained by Aman.

Is this solution Helpfull? Yes (3) | No   

Vignesh  (12 years ago)

If anybody have easy explanation to solve this question.
Take my answer as reference and worked out.
Thank you:)

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