document.write( "Question 372984: How do I solve log(x-5)+log(x+3)=2? \n" ); document.write( "

Algebra.Com's Answer #265584 by robertb(5830) $\"\"$ $\"About$

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The given equation is the same as $\"log%28%28x-5%29%28x%2B3%29%29+=+2\"$ , or
\n" ); document.write( " $\"log%28%28x%5E2-2x-15%29%29+=+2\"$ , or
\n" ); document.write( " $\"x%5E2+-+2x+-+15+=+10%5E2\"$ . Simplifying,
\n" ); document.write( " $\"x%5E2-2x+-+115+=+0\"$ ,\r
\n" ); document.write( "\n" ); document.write( " $\"x+=+%282%2B-+sqrt%28%28-2%29%5E2-4%2A1%2A-115%29%29%2F2%29+\"$ ,
\n" ); document.write( " $\"x+=+%282%2B-+sqrt%28464%29%29%2F2%29\"$ ,\r
\n" ); document.write( "\n" ); document.write( " $\"x+=+%282%2B-+4sqrt%2829%29%29%2F2%29\"$ ,
\n" ); document.write( " $\"x+=+1%2B-+2sqrt%2829%29\"$ .\r
\n" ); document.write( "\n" ); document.write( "Only the root $\"1%2B2sqrt%2829%29\"$ will satisfy the original equation.\r
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