If 8^{x}9^{2y}=81(2^{12y}), what is the value of x?

Question

If  8^{x}9^{2y}=81(2^{12y}) , what is the value of x?

(A) 2
(B) 4
(C) 8
(D) 12
(E) 16

Kudos for a correct  solution .

KS15 · Answer

2^3x*3^4y=3^4*2^12y
Equating powers with equal bases,
3x=12y &4y=4
y=1
Therefore, 3x=12
x=4
Answer B

noTh1ng · Answer

How is it possible to equate the bases ? They are not the same throughout the equation

kunal555 · Answer

8^{x}9^{2y}=81(2^{12y})

or  8^{x}9^{2y}=9^2(8^{4y})

So,
2y=2
or y=1

Also,
x=4y
or x=4

Answer:-B

ENGRTOMBA2018 · Answer

Good question. This is the reason you need to do the prime factorization of the "big" numbers

Recognise that 8 =  2^3 
9 =  3^2 
81= 3^4

So now, you will have the bases either with 2s or 3s. Then equation the powers of 2s on either side of the equations and similarly equate the powers of 3s on either side.

anudeep133 · Answer

Solution:

change all bases into 2 and 3.
Then, we get 4y=4 and 3x= 12y.
So, y=1 and x=4.
So, answer is B

harishbiyani8888 · Answer

Making the same base on both the sides of equations we get (2^3x) x 9^2y = (2^12y) x 9^2

Equating the common bases,

1) 3x = 12y and 2) 2y = 2, there fore y =1 substituting in 1 we get x = 4

Correct answer is B

Bunuel · Answer

VERITAS PREP OFFICIAL SOLUTION:

In this problem, break down the larger numbers to find common bases for the exponents.  8^{x}  can be written as  (2^{3})^{x}  and 81 can be written as  9^{2} , yielding  (2^{3})^{x} * 9^{2y} = 9^{2}(2^{12y}) . Because we now have common bases for the 9s, we can ignore  (2^3)^x  and  2^{12y}  because 2 to any power does not share any factors with 9 to any power (since 9 = 3 x 3). Therefore, we can determine that 2y = 2, and that y = 1.

Plugging in for the 2 terms, we then have  (2^{3})^{x} = 2^{12} .

As an exponential rule,  (2^{3})^{x}  is equal to  2^{3x} , so we can again set the exponents with same bases equal to find that  3x = 12 , and that  x = 4 .

Answer: B.

kunlmhjn · Answer

8^{x}9^{2y}=81(2^{12y})
(2^3x)(9^2y)=(9^2)(2^12y)
(2^3x)(9^2y)=(2^12y)(9^2)

As we know if the bases are same then EXPONENTS are equal. Therefore,
Base '9' EXPONENTS i.e 2y=2,
we get y=1

Similarly, For base '2'

3x=12y
x=4y
but we got y=1 therefore, x=4

Hence Answer is B
:-D

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If 8^{x}9^{2y}=81(2^{12y}), what is the value of x?

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If 8^{x}9^{2y}=81(2^{12y}), what is the value of x?

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