document.write( "Question 377744: Solve the equation
\n" ); document.write( "log(x+1)-log(x+2)=log(1/x) \n" ); document.write( "

Algebra.Com's Answer #268421 by robertb(5830) $\"\"$ $\"About$

You can put this solution on YOUR website!
The equation becomes:
\n" ); document.write( " $\"log%28%28x%2B1%29%2F%28x%2B2%29%29+=+log%281%2Fx%29\"$ ;
\n" ); document.write( " $\"%28x%2B1%29%2F%28x%2B2%29+=+1%2Fx\"$ , since log is a one-to-one function.
\n" ); document.write( "x(x+1) = x+2, after cross-multiplication.
\n" ); document.write( " $\"x%5E2+%2B+x+=+x%2B2\"$ ,or
\n" ); document.write( " $\"x%5E2+=+2\"$ , or $\"x+=+-sqrt%282%29\"$ or $\"x+=+sqrt%282%29\"$ . The first value will NOT satisfy the original equation, and so the final answer is $\"x+=+sqrt%282%29\"$ . \n" ); document.write( "

\n" );