document.write( "Question 56747: I having trouble solving this equation
\n" ); document.write( "log (x+3)=1-log x \n" ); document.write( "

Algebra.Com's Answer #38507 by funmath(2933) $\"\"$ $\"About$

You can put this solution on YOUR website!
The rules we are going to use are:
\n" ); document.write( " $\"highlight%28log%28a%29%2Blog%28b%29=log%28a%2Ab%29%29\"$
\n" ); document.write( " $\"highlight%28log%28a%29=m%29\"$ ==>> $\"highlight%2810%5Em=a%29\"$
\n" ); document.write( " $\"log%28%28x%2B3%29%29=1-log%28%28x%29%29\"$
\n" ); document.write( " $\"log%28%28x%29%29%2Blog%28%28x%2B3%29%29=1-log%28%28x%29%29%2Blog%28%28x%29%29\"$
\n" ); document.write( " $\"log%28%28x%29%29%2Blog%28%28x%2B3%29%29=1\"$
\n" ); document.write( " $\"log%28x%28x%2B3%29%29=1\"$
\n" ); document.write( " $\"10%5E1=x%28x%2B3%29\"$
\n" ); document.write( " $\"10=x%5E2%2B3x\"$
\n" ); document.write( " $\"-10%2B10=x%5E2%2B3x-10\"$
\n" ); document.write( " $\"0=x%5E2%2B3x-10\"$ Factor:
\n" ); document.write( "0=(x__)(x___)
\n" ); document.write( "We need to fill the blanks with two integers that multiply to give us:-10, but add to give us:+3
\n" ); document.write( "5*(-2)=-10 and 5-2=+3
\n" ); document.write( "0=(x+5)(x-2)
\n" ); document.write( "x+5=0 and x-2=0
\n" ); document.write( "x=-5 and x=2
\n" ); document.write( "We have to check for extraneous solutions:
\n" ); document.write( " $\"log%28-5%2B3%29=1-log%28-5%29\"$ x=-5 is extraneous, because we can't take the log of a negative number.
\n" ); document.write( " $\"log%282%2B3%29=1-log%282%29\"$
\n" ); document.write( " $\"log%285%29=1-log%282%29\"$
\n" ); document.write( " $\".6989700043=.698700043\"$
\n" ); document.write( "x=2 is a solution.
\n" ); document.write( "Happy Calculating!!!
\n" ); document.write( " \n" ); document.write( "

\n" );