document.write( "Question 22212: Simplify:
\n" ); document.write( " $\"log%28+7%2C+5x%29+-+log%28+7%2C+x%2B3%29+=+4log%28+7%2C+3%29\"$ \n" ); document.write( "

Algebra.Com's Answer #10764 by Earlsdon(6294) $\"\"$ $\"About$

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Simplify:
\n" ); document.write( " $\"log%287%2C%285x%29%29+-+log%287%2C%28x%2B3%29%29+=+4log%287%2C%283%29%29\"$ Apply the Quotient rule for logarithms: $\"log%28b%2CM%29-log%28b%2CN%29+=+log%28b%2C%28M%2FN%29%29\"$ to the left side. The right side is rewritten because: $\"log%28b%2CM%5Ep%29+=+p%2Alog%28b%2CM%29\"$
\n" ); document.write( " $\"log%287%2C%285x%2F%28x%2B3%29%29%29+=+log%287%2C%283%5E4%29%29\"$ If $\"log%28b%2CM%29+=+log%28b%2CN%29\"$ then $\"M=N\"$ , so:
\n" ); document.write( " $\"5x%2F%28x%2B3%29+=+3%5E4\"$
\n" ); document.write( " $\"5x%2F%28x%2B3%29+=+81\"$ Multiply both sides by (x+3)
\n" ); document.write( " $\"5x+=+81x+%2B+243\"$ Subtract 243 from both sides.
\n" ); document.write( " $\"5x-243+=+81x\"$ Subtract 5x from both sides.
\n" ); document.write( " $\"-243+=+76x\"$ Divide both sides by 76.
\n" ); document.write( " $\"x+=+-3.197368\"$ \r
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