document.write( "Question 132012: how can i solve \r
\n" ); document.write( "\n" ); document.write( "logX + logX + 1 = log12 ? \n" ); document.write( "

Algebra.Com's Answer #96403 by josmiceli(19441) $\"\"$ $\"About$

You can put this solution on YOUR website!
$\"log%28X%29+%2B+log%28X%29+%2B+1+=+log%2812%29\"$
\n" ); document.write( "First get everything in terms of logs
\n" ); document.write( "1 = log(x)
\n" ); document.write( "If the base is $\"10\"$ , then I can write
\n" ); document.write( " $\"10%5E1+=+x\"$
\n" ); document.write( " $\"x+=+10\"$ , so
\n" ); document.write( " $\"1+=+log%2810%29\"$
\n" ); document.write( "Now rewrite it
\n" ); document.write( " $\"log%28X%29+%2B+log%28X%29+%2B+log%2810%29+=+log%2812%29\"$
\n" ); document.write( "The general rule for logs is:
\n" ); document.write( " $\"log%28a%2Ab%2Ac%29+=+log%28a%29+%2B+log%28b%29+%2B+log%28c%29\"$ so,
\n" ); document.write( " $\"log%28X%29+%2B+log%28X%29+%2B+log%2810%29+=+log%28X%2AX%2A10%29\"$
\n" ); document.write( " $\"log%2810x%5E2%29+=+log%2812%29\"$
\n" ); document.write( "If the logs are equal, the numbers are equal
\n" ); document.write( " $\"10X%5E2+=+12\"$
\n" ); document.write( " $\"X%5E2+=+6%2F5\"$
\n" ); document.write( " $\"X+=+sqrt%286%2F5%29\"$ answer
\n" ); document.write( "There is a negative square root also, but it makes
\n" ); document.write( "no sense here, since there is no log to the base 10
\n" ); document.write( "that will give me a negative number
\n" ); document.write( "check:
\n" ); document.write( " $\"sqrt%286%2F5%29+=+1.0954\"$
\n" ); document.write( " $\"log%28X%29+%2B+log%28X%29+%2B+1+=+log%2812%29\"$
\n" ); document.write( " $\"log%281.0954%29+%2B+log%281.0954%29+%2B+1+=+log%2812%29\"$
\n" ); document.write( " $\".03957+%2B+.03957+%2B+1+=+1.0792\"$
\n" ); document.write( " $\".07914+%2B+1+=+1.0792\"$
\n" ); document.write( " $\"1.07914+=+1.0792\"$
\n" ); document.write( "close enough
\n" ); document.write( " \n" ); document.write( "

\n" );