1972 AHSME Problems/Problem 8
Revision as of 21:46, 28 January 2021 by Coolmath34 (talk | contribs) (Created page with "== Problem == If <math>|x-\log y|=x+\log y</math> where <math>x</math> and <math>\log y</math> are real, then <math>\textbf{(A) }x=0\qquad \textbf{(B) }y=1\qquad \textbf{(C)...")
Problem
If 
where 
and 
are real, then
Solution
We have two cases: is positive and is negative.
![\[\text{Positive} \qquad x - \log y = x + \log y \qquad \rightarrow \qquad 2\log y = 0 \rightarrow y = 1\]](http://latex.artofproblemsolving.com/f/8/6/f86e07958a8d3a13740c82630ce5f8f83b8131e3.png)
![\[\text{Negative} \qquad -x + \log y = x + \log y \qquad \rightarrow \qquad 2x = 0 \rightarrow x = 0\]](http://latex.artofproblemsolving.com/e/d/5/ed5c9974dcfa48b42e5042f8f8c07f12f1a5a9b5.png)
We can write 
to show that 
or both.
The answer is 
-edited by coolmath34
