Question 1147951
<br>
NO!  The two solutions do NOT both work!<br>
The given equation is<br>
(1) log(x − 3) − log(5x − 7) = log(1/x)<br>
To start solving that, you use rules of logarithms:<br>
(2) log((x-3)/(5x-7)) = log(1/x)<br>
Working from there, you find apparent solutions x=1 and x=7.<br>
And those solutions both work in (2).<br>
BUT... they have to satisfy the ORIGINAL equation.  And x=1 does not, because it results in trying to take the logarithm of a negative number.<br>
ANSWER: x=7 is the only solution.<br>