document.write( "Question 67199This question is from textbook
\n" ); document.write( ": help me solve ln(x^2 + 12)=ln x + ln 8 \n" ); document.write( "

Algebra.Com's Answer #47771 by bam878s(77) $\"\"$ $\"About$

You can put this solution on YOUR website!
This problem is simple once you utilize a common law of logarithms.\r
\n" ); document.write( "\n" ); document.write( "ln ab = ln a + ln b\r
\n" ); document.write( "\n" ); document.write( "On the right hand side of this equation we have ln x + ln 8. By using the above law, we can write this as ln 8x.\r
\n" ); document.write( "\n" ); document.write( "So, we have:
\n" ); document.write( "ln( $\"x%5E2\"$ + 12) = ln 8x. So now we know that $\"x%5E2\"$ + 12 = 8x\r
\n" ); document.write( "\n" ); document.write( " $\"x%5E2\"$ + 12 = 8x
\n" ); document.write( " $\"x%5E2\"$ + 12 - 8x = 0
\n" ); document.write( " $\"x%5E2\"$ - 8x + 12 = 0. We can solve this by using the quadratic formula, but an easier way would be to factor this out as follows:\r
\n" ); document.write( "\n" ); document.write( " $\"x%5E2\"$ - 8x + 12 = (x-6) * (x-2). So, we have:\r
\n" ); document.write( "\n" ); document.write( "(x-6)(x-2) = 0. We know that 0 * anything = 0, so now we can easily see that
\n" ); document.write( "x = 6 or x = 2. \r
\n" ); document.write( "\n" ); document.write( "Hope this helps!! \n" ); document.write( "

\n" );