document.write( "Question 113499: How can I write the expression 2.1n x-1n y+3. 1n z as a single lograithm. The periods after the 2 and 3 stands for the (times) sign not periods.\r
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Algebra.Com's Answer #82582 by solver91311(24713) $\"\"$ $\"About$

You can put this solution on YOUR website!
$\"2%2Aln%28x%29-ln%28y%29%2B3%2Aln%28z%29\"$ \r
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\n" ); document.write( "\n" ); document.write( "First rule to apply is that $\"a%2Aln%28x%29=ln%28x%5Ea%29\"$ , so we can write:\r
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\n" ); document.write( "\n" ); document.write( " $\"ln%28x%5E2%29%2Bln%28y%5E%28-1%29%29%2Bln%28z%5E3%29\"$
\n" ); document.write( " $\"ln%28x%5E2%29%2Bln%281%2Fy%29%2Bln%28z%5E3%29\"$ \r
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\n" ); document.write( "\n" ); document.write( "The next rule is that the log of the product is the sum of the logs of the factors, like this:\r
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\n" ); document.write( "\n" ); document.write( " $\"ln%28abc%29=ln%28a%29%2Bln%28b%29%2Bln%28c%29\"$ . So for this problem:\r
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\n" ); document.write( "\n" ); document.write( " $\"ln%28x%5E2%29%2Bln%281%2Fy%29%2Bln%28z%5E3%29=ln%28x%5E2z%5E3%2Fy%29\"$ \r
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\n" ); document.write( "\n" ); document.write( "Hope this helps,
\n" ); document.write( "John\r
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\n" ); document.write( "\n" ); document.write( "P.S. Next time use the asterisk '*' (Shift-8) to make the multiplication sign as in 2 * 3 = 6 \n" ); document.write( "

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