Is 4^x+y = 8^10?

[ER]

Hello,

Is 4^x+y = 8^10?

Statement 1: x-y=9

The book states that this is NOT sufficient. However, I did the following calculations and am wondering where I went wrong. Based on the below, wouldn't statement one be sufficient?

1. Re-arrange the equation: x=y+9

2. Break down the bases in the question stem:
a) 4^x+y = 2^2(x+y) = 2^2x+2y
b) 8^10 = 2^30

3. Get rid of the bases since they're now equal: 2x+2y = 30

4. Substitute out x and input y+9: 2(y+9)+2y = 30. Solving for y, you get y = 3.

5. Then, plug is 3 for y
a) 2^2(y+9)+2y = 2^2y+18+2y = 2^4y+18 = 2^4(3)+18 = 2^30, which is equals 2^30 or 8^10.

Maybe I'm missing something really obvious, I'm wondering where I went wrong.

Thank you in advance.

[RonPurewal]

the problem is that, when you were manipulating the question, you dropped the "is" and the "?".

then, after those were gone, you totally forgot that you were working with the question, not with a statement.

[RonPurewal]

here's what you should have written:

2. Break down the bases in the question stem:
a) 4^x+y = 2^2(x+y) = 2^2x+2y
b) 8^10 = 2^30

3. Get rid of the bases since they're now equal:
Is 2x+2y = 30?

this is a question, not a statement. so, the question boils down to "is x + y = 15?".

now try re-working the problem.

... and, in future problems, ALWAYS keep "is" and "?" when you manipulate questions.

[ER]

Thanks!

[RonPurewal]

sure.