document.write( "Question 473030: Solve the logarithmic equation. Express your solutions in exact form only.
\n" ); document.write( "In(3x+5)+In(3x-5)=6+In4 \n" ); document.write( "

Algebra.Com's Answer #324340 by Tatiana_Stebko(1539) $\"\"$ $\"About$

You can put this solution on YOUR website!
$\"ln%283x%2B5%29%2Bln%283x-5%29=6%2Bln4\"$
\n" ); document.write( " $\"system%283x%2B5%3E0%2C+3x-5%3E0%29\"$ => $\"system%283x%3E-5%2C++3x%3E5%29\"$ => $\"system%28x%3E-5%2F3%2C++x%3E5%2F3%29\"$ => $\"x%3E5%2F3\"$
\n" ); document.write( "Let write 6 in the way $\"6=ln%28e%5E6%29\"$
\n" ); document.write( " $\"ln%283x%2B5%29%2Bln%283x-5%29=ln%28e%5E6%29%2Bln4\"$
\n" ); document.write( "Use formula $\"lna%2Blnb=ln%28ab%29\"$
\n" ); document.write( " $\"ln%28%283x%2B5%29%283x-5%29%29=ln%284e%5E6%29\"$
\n" ); document.write( " $\"%283x%2B5%29%283x-5%29=4e%5E6\"$
\n" ); document.write( "Use formula $\"%28a%2Bb%29%28a-b%29=a%5E2-b%5E2\"$
\n" ); document.write( " $\"9x%5E2-25=4e%5E6\"$ add 25 to the both sides
\n" ); document.write( " $\"9x%5E2=4e%5E6%2B25\"$ divide by 9
\n" ); document.write( " $\"x%5E2=%284e%5E6%2B25%29%2F9\"$
\n" ); document.write( " $\"x1=sqrt%28%284e%5E6%2B25%29%2F9%29\"$
\n" ); document.write( " $\"x2=-sqrt%28%284e%5E6%2B25%29%2F9%29%3C5%2F3\"$ extraneous root
\n" ); document.write( "Answer $\"x=sqrt%28%284e%5E6%2B25%29%2F9%29\"$ \n" ); document.write( "

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