If 8x = 16^y, what is y in terms of x?

Question

If 8x =  16^y , what is x in terms of y?

(A)  2^y

(B)  2^ {2y - 3}

(C)  2^ {3y - 4}

(D)  2^ {4y - 2}

(E)  2^ {4y – 3}

Mona2019 · Answer

Is it X in terms of y or y in terms of X.
X in terms of y . Gives 2^(4y-3)
Which is obtained by simplifying to the powers of 2 in both LHS and RHS.

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Vvin · Answer

2^3 x = 2^4y

x = 2^4y / 2^3
x= 2^4y * 2^-3

x= 2^4y-3

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chrtpmdr · Answer

The prompt is wrong, isn't it? Answer should express Y in terms of X and not X in terms of Y, or am I mistaken?

Bunuel · Answer

___________________
Yes. Edited. Thank you.

JHANZ · Answer

Vvin how did you go from x = 2^4y / 2^3 to x= 2^4y * 2^-3?
Dont the exponents 4y just minus 3?
I dont quite follow but i believe im missing something.

*edit
is it because exponent 4y cannot minus 3 thus it would be 2^4y-3

thanks

MathRevolution · Answer

8x = 16^y

=> x =  \frac{16^y }{ 8}

=> x =  \frac{(2^4)^y }{ (2^3)}

=> x =  \frac{(2^{4y})}{ (2^3)}

=> x =  (2^{4y -3})

Answer E

Abhishek009 · Answer

2^3*x = 2^{4y}

So,  x = 2^{4y - 3} , Answer is clearly (E)

Abhishek009 · Answer

8x = 16^y

Or,  2^3*x = 2^{4y}

Or,  x = 2^{4y-3} , Answer will be (E)

If 8x = 16^y, what is y in terms of x?

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If 8x = 16^y, what is y in terms of x?

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