document.write( "Question 507520: solve log(3x+4)=2log(x) \n" ); document.write( "

Algebra.Com's Answer #340515 by Earlsdon(6294) $\"\"$ $\"About$

You can put this solution on YOUR website!
Solve:
\n" ); document.write( " $\"Log%283x%2B4%29+=+2Log%28x%29\"$ Apply the \"power rule\" to the right side.
\n" ); document.write( " $\"Log%283x%2B4%29+=+Log%28x%5E2%29\"$ Now if $\"Log%28M%29+=+Log%28N%29\"$ then $\"M+=+N\"$ so...
\n" ); document.write( " $\"3x%2B4+=+x%5E2\"$ Rearrange as:
\n" ); document.write( " $\"x%5E2-3x-4+=+0\"$ Solve by factoring:
\n" ); document.write( " $\"%28x%2B1%29%28x-4%29+=+0\"$ Apply the \"zero product\" rule:
\n" ); document.write( " $\"x%2B1+=+0\"$ or $\"x-4+=+0\"$ so that...
\n" ); document.write( " $\"x+=+-1\"$ or $\"x+=+4\"$
\n" ); document.write( "Now you must check the results for \"extraneous\" or \"invalid\" values:
\n" ); document.write( "Try $\"x+=+-1\"$
\n" ); document.write( " $\"Log%283x%2B4%29+=+2Log%28x%29\"$ Substitute $\"x+=+-1\"$
\n" ); document.write( " $\"Log%283%28-1%29%2B4%29+=+2Log%28-1%29\"$
\n" ); document.write( " $\"Log%281%29+=+2Log%28-1%29\"$
\n" ); document.write( " $\"0+=+2%281.364376%29i\"$ This is not valid!
\n" ); document.write( "Try $\"x+=+4\"$
\n" ); document.write( " $\"Log%283x%2B4%29+=+2Log%28x%29\"$ Substitute $\"x+=+4\"$
\n" ); document.write( " $\"Log%2816%29+=+2Log%284%29\"$
\n" ); document.write( " $\"1.20411998+=+2%280.60205999%29\"$
\n" ); document.write( " $\"1.20411998+=+1.20411998\"$ This is valid.
\n" ); document.write( "Solution is $\"x+=+4\"$ \n" ); document.write( "

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