The solution to the problem is as follows:
Then,
<span>
log2 x/(x-7)=3 </span>
<span>
x/(x-7)=8 </span>
<span>
x=8x-56 </span>
<span>
-7x=-56 </span>
<span>
x=8
</span>
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2x+7=11-2x (add 2x)
4x+7=11 (minus 7)
4x=4 (divide by 4)
x=1
Answer:
The smaller number is 4√2 and the larger number is (4√2 + 1).
Step-by-step explanation:
Let the two numbers be <em>x </em>and <em>y</em>, where <em>y</em> is the larger of the two numbers.
Since <em>y</em> is the larger number, it is one more than the smaller number. So:

When negative two times the smaller is added to the square of the larger, the result is 33. In other words:

Substitute:

Solve for <em>x</em>. Square:

Simplify:

Subtract one from both sides:

And take the square root of both sides:

Since <em>y</em> is positive, we can ignore the negative case. So, the smaller number is:

And the larger number is:

You are correct because all students in the class may not be taking a test.