document.write( "Question 54934: PLEASE HELP ME WITH THIS PROBLEM;
\n" ); document.write( "solve the equation In(x+5)- In(3)= In (x-3) \n" ); document.write( "

Algebra.Com's Answer #37125 by funmath(2933) $\"\"$ $\"About$

You can put this solution on YOUR website!
The rules we're going to use are:
\n" ); document.write( "1. $\"highlight%28ln%28a%29-ln%28b%29=ln%28a%2Fb%29%29\"$
\n" ); document.write( "2. $\"highlight%28ln%28a%29=b%29\"$ => $\"highlight%28a=e%5Eb%29\"$
\n" ); document.write( "3. $\"highlight%28a%5E0=1%29\"$
\n" ); document.write( "solve the equation ln(x+5)- ln(3)= ln (x-3)
\n" ); document.write( " $\"ln%28x%2B5%29-ln%283%29-ln%28x-3%29=ln%28x-3%29-ln%28x-3%29\"$
\n" ); document.write( " $\"ln%28x%2B5%29-ln%283%29-ln%28x-3%29=0\"$
\n" ); document.write( " $\"ln%28%28x%2B5%29%2F%283%28x-3%29%29%29=0\"$ Rule 1
\n" ); document.write( " $\"%28x%2B5%29%2F%283%28x-3%29%29=e%5E0\"$ Rule 2
\n" ); document.write( " $\"%28x%2B5%29%2F%283%28x-3%29%29=1\"$ Rule 3
\n" ); document.write( " $\"3%28x-3%29%28x%2B5%29%2F%283%28x-3%29%29=3%28x-3%29%281%29\"$
\n" ); document.write( " $\"cross%283%28x-3%29%29%28x%2B5%29%2Fcross%283%28x-3%29%29=3%28x-3%29\"$
\n" ); document.write( " $\"x%2B5=3x-9\"$
\n" ); document.write( " $\"-x%2Bx%2B5=-x%2B3x-9\"$
\n" ); document.write( " $\"5=2x-9\"$
\n" ); document.write( " $\"9%2B5=2x-9%2B9\"$
\n" ); document.write( " $\"14=2x\"$
\n" ); document.write( " $\"14%2F2=2x%2F2\"$
\n" ); document.write( " $\"7=x\"$
\n" ); document.write( ":
\n" ); document.write( "Check by subtituting 7 in for x's in the original equation and see if both sides equal once you simplify:
\n" ); document.write( " $\"ln%287%2B5%29-ln%283%29=ln%287-3%29\"$
\n" ); document.write( " $\"ln%2812%29-ln%283%29=ln%284%29\"$
\n" ); document.write( " $\"ln%2812%2F3%29=ln%284%29\"$ Rule 1
\n" ); document.write( " $\"ln%284%29=ln%284%29\"$ We're right!!!
\n" ); document.write( "Happy Calculating!!! \n" ); document.write( "

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