document.write( "Question 85549This question is from textbook Blitzer
\n" ); document.write( ": Help on this one....what am I to solve to get the answer?\r
\n" ); document.write( "\n" ); document.write( "Solve the equation(not in book).
\n" ); document.write( "4) log (3 + x) - log (x - 3) = log 3
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Algebra.Com's Answer #61794 by bucky(2189) $\"\"$ $\"About$

You can put this solution on YOUR website!
Given:
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\n" ); document.write( " $\"log%28%283%2Bx%29%29+-+log%28%28x-3%29%29+=+log%283%29\"$
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\n" ); document.write( "Notice that the left side has the difference of two logs. By the rules of logs this can
\n" ); document.write( "be written as the log of the division of the two quantities that the log is operating
\n" ); document.write( "on, the numerator being from the positive log and the denominator being from the negative
\n" ); document.write( "log. Following this rule the equation becomes:
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\n" ); document.write( " $\"log%28%28%283%2Bx%29%2F%28x-3%29%29%29+=+log%283%29\"$
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\n" ); document.write( "Note that for this equation to be true the quantities in the parentheses on both sides of
\n" ); document.write( "the equal sign must be equal. In other words, for the left side of this equation to be equal to
\n" ); document.write( "the right side, the log operator must be acting on equal quantities on both sides.
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\n" ); document.write( "This being the case, you can write the new equation:
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\n" ); document.write( " $\"%283%2Bx%29%2F%28x-3%29+=+3\"$
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\n" ); document.write( "Get rid of the denominator by multiplying both sides of this equation by (x - 3). When
\n" ); document.write( "you do the equation becomes:
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\n" ); document.write( " $\"3%2Bx+=+3%2A%28x-3%29\"$
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\n" ); document.write( "Multiplying out the right side leads to the equation:
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\n" ); document.write( " $\"3+%2B+x+=+3x+-+9\"$
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\n" ); document.write( "Get rid of the 3x on the right side by subtracting 3x from both sides to get:
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\n" ); document.write( " $\"3+-+2x+=+-9\"$
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\n" ); document.write( "and then eliminate the 3 on the left side by subtracting 3 from both sides:
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\n" ); document.write( " $\"+-2x+=+-12\"$
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\n" ); document.write( "Finally, solve for x by dividing both sides by -2:
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\n" ); document.write( " $\"x+=+-12%2F-2+=+6\"$
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\n" ); document.write( "Check to ensure this is correct by returning to the original problem and substituting
\n" ); document.write( "6 for x:
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\n" ); document.write( " $\"log%28%283%2Bx%29%29+-+log%28%28x-3%29%29+=+log%283%29\"$
\n" ); document.write( ".
\n" ); document.write( " $\"log%28%283%2B6%29%29+-+log%28%286-3%29%29+=+log%283%29\"$
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\n" ); document.write( " $\"log%289%29+-+log%283%29+=+log%283%29\"$
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\n" ); document.write( "and applying the rule for the difference of the two logs on the left side:
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\n" ); document.write( " $\"log%28%289%2F3%29%29+=+log%283%29\"$
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\n" ); document.write( "which simplifies to:
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\n" ); document.write( " $\"log%283%29+=+log%283%29\"$
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\n" ); document.write( "Since this is obviously true, we have a correct solution in x = +6.
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\n" ); document.write( "Hope this helps you to understand the problem. \n" ); document.write( "

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