document.write( "Question 827710: log(x-4) = -2 + log(x+3) \n" ); document.write( "

Algebra.Com's Answer #498834 by LinnW(1048) $\"\"$ $\"About$

You can put this solution on YOUR website!
$\"log%28%28x-4%29%29+=+-2+%2B+log%28%28x%2B3%29%29\"$
\n" ); document.write( "log(1/100) = -2 since $\"%2810%5E%28-2%29%29\"$ = $\"%281%2F%2810%5E2%29%29\"$ = $\"%281%2F100%29\"$
\n" ); document.write( "so $\"log%28%28x-4%29%29+=+-2+%2B+log%28%28x%2B3%29%29\"$ = $\"log%28%28x-4%29%29+=+log%281%2F100%29+%2B+log%28%28x%2B3%29%29\"$
\n" ); document.write( "This solution assumes that log means log base 10.
\n" ); document.write( " $\"log%28%28x-4%29%29+=+log%28%28%281%2F100%29%2A%28x%2B3%29%29%29\"$
\n" ); document.write( "so x-4 = (1/100)*(x+3)
\n" ); document.write( "multiply each side by 100
\n" ); document.write( "100(x-4) = x+3
\n" ); document.write( "100x - 400 = x + 3
\n" ); document.write( "add 400 to each side
\n" ); document.write( "100x = x + 403
\n" ); document.write( "subtract x from each side
\n" ); document.write( "99x = 403
\n" ); document.write( " x = 403/99
\n" ); document.write( "Let's see if it works
\n" ); document.write( "log((x-4)) = -2 + log((x+3))
\n" ); document.write( "add 2 - log((x+3)) to each side
\n" ); document.write( "log((x-4)) - log((x+3)) = -2
\n" ); document.write( "rewriting the the left hand side and plugging into excel we can
\n" ); document.write( "verify that
\n" ); document.write( "log10(403/99 - 4) - log10( 403/99 + 3) = -2 \n" ); document.write( "

\n" );