Question 105757
<pre>
Solve logx + log(x-48) = 2
**************************<font color = blue><font size = 2><font face = tahoma><b>
As usual, HyperBrain(694)'s solution is PARTIALLY-CORRECT/WRONG.
Furthermore, the TRINOMIAL, {{{x^2 - 48x - 100}}} can be factorized into (x - 50)(x + 2), so, using the QUADRATIC EQUATION formula is UNNECESSARY,
as it NOTICEABLY generates LARGE numbers, which most of us deplore!! Unless, of course, one wishes to do so! 

log (x) + log (x - 48) = 2
Finally, as the SMALLER of the 2 log variable-arguments, x - 48 MUST be > 0, we get: x - 48 > 0_____x > 48.
So, equation becomes: log (x) + log (x - 48) = 2, with x > 48.

One of the respondent's 2 solutions, - 2 is NOT > 48, which makes it, EXTRANEOUS. Obviously, the other solution, x = 50 is EFINITELY > 48, making
it VALID/ACCEPTABLE, and therefore, the SOLE SOLUTION.</font></font></font></b></pre>