document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=25293>Question 25293</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Solve each logarithmic equation. Check each solution.\r<BR>\n" );
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document.write( "1. log 3x=2         2. 4log x=4      3. log(3x-2)=3           4. 2logx -log5=-2\r<BR>\n" );
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document.write( "5. log 8 - log 2x=-1    6. log(x+21)+logx=2        \r<BR>\n" );
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document.write( "I have a hard time understanding algebra period because of lack of training that was given to me. So you coul be my permanet helper if you like!.! It's six problems if you wouldn't mind.<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #13547 by </B><A HREF=/tutors/aboutme.mpl?userid=AnlytcPhil><B>AnlytcPhil(1807)</B></A><img src=\"/images/stars/stars-12.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=AnlytcPhil><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/cgi-bin/show-face.mpl?user=AnlytcPhil><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=13547\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <PRE STYLE=\"white-space: pre-wrap; white-space: -moz-pre-wrap; white-space: -pre-wrap; white-space: -o-pre-wrap; word-wrap: break-word;\"><font face = \"lucida console\" size = 3>><b>\r\n" );
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document.write( "1. log(3x) = 2\r\n" );
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document.write( "For that you need to know that an equation of the form\r\n" );
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document.write( " log(A) = B  can be written as A = 10<sup>B</sup>.  You should memorize this rule.\r\n" );
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document.write( "here A = 3x and B = 2, so rewrite log(3x) = 2 as 3x = 10<sup>2</sup>\r\n" );
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document.write( "3x = 10<sup>2</sup>\r\n" );
document.write( "3x = 100\r\n" );
document.write( " x = 100/3 or 33 1/3\r\n" );
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document.write( " 2.  4log(x) = 4 \r\n" );
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document.write( "First divide both sides by 4\r\n" );
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document.write( "      log(x) = 1\r\n" );
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document.write( "Now use the same rule used in problem 1 to rewrite that equation as\r\n" );
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document.write( "      x = 10<sup>1</sup> \r\n" );
document.write( "      x = 10\r\n" );
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document.write( "3. log(3x - 2) = 3\r\n" );
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document.write( "Use the same rule to rewrite that as\r\n" );
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document.write( "       3x - 2 = 10<sup>3</sup>\r\n" );
document.write( "       3x - 2 = 1000\r\n" );
document.write( "           3x = 1002\r\n" );
document.write( "            x = 1002/3\r\n" );
document.write( "            x = 334         \r\n" );
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document.write( " 4. 2log(x) - log(5) = -2\r\n" );
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document.write( "  Here you need the rule\r\n" );
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document.write( " A·log(B) = log(B<sup>A</sup>)\r\n" );
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document.write( " to rewrite 2log(x) as log(x<sup>2</sup>)\r\n" );
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document.write( "   log(x<sup>2</sup>) - log(5) = -2\r\n" );
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document.write( " Now you need the rule\r\n" );
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document.write( "   log(A) - log(B) = log(A/B)\r\n" );
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document.write( " to rewrite the left side as log(x<sup>2</sup>/5) = -2\r\n" );
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document.write( "  log(x<sup>2</sup>/5) = -2\r\n" );
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document.write( "Now us the rule we used in previous problems to write that equation as\r\n" );
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document.write( "  x<sup>2</sup>/5 = 10<sup>-2</sup>\r\n" );
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document.write( "Now use the rule A<sup>-B</sup> = 1/A<sup>B</sup> to rewrite the right side\r\n" );
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document.write( "  x<sup>2</sup>/5 = 1/10<sup>2</sup>\r\n" );
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document.write( "  x<sup>2</sup>/5 = 1/100\r\n" );
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document.write( "Multiply both sides by 100\r\n" );
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document.write( " 100·x<sup>2</sup>/5 = 100·1/100\r\n" );
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document.write( "     20x<sup>2</sup> = 1\r\n" );
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document.write( "       x<sup>2</sup> = 1/20\r\n" );
document.write( "              ____\r\n" );
document.write( "        x = ±<font face=\"symbol\">Ö</font>1/20 \r\n" );
document.write( "                __ \r\n" );
document.write( "        x = ±1/<font face=\"symbol\">Ö</font>20 \r\n" );
document.write( "                 ___\r\n" );
document.write( "        x = ±1/(<font face=\"symbol\">Ö</font>4·5)\r\n" );
document.write( "                  _ \r\n" );
document.write( "        x = ±1/(2<font face=\"symbol\">Ö</font>5)\r\n" );
document.write( "                   _    _  _\r\n" );
document.write( "        x = [±1/(2<font face=\"symbol\">Ö</font>5)][<font face=\"symbol\">Ö</font>5/<font face=\"symbol\">Ö</font>5]\r\n" );
document.write( "              _\r\n" );
document.write( "        x = ±<font face=\"symbol\">Ö</font>5/(2·5)\r\n" );
document.write( "              _\r\n" );
document.write( "        x = ±<font face=\"symbol\">Ö</font>5/10\r\n" );
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document.write( "We discard the negative answer, because we cannot take logarithms of\r\n" );
document.write( "negative numbers.  So the answer is\r\n" );
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document.write( "        x = <font face=\"symbol\">Ö</font>5/10\r\n" );
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document.write( "5. log(8) - log(2x) = -1 \r\n" );
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document.write( "   Use the rule\r\n" );
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document.write( "   log(A) - log(B) = log(A/B) to rewrite the LHS\r\n" );
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document.write( "   log[8/(2X)] = -1\r\n" );
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document.write( "      log(4/X) = -1\r\n" );
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document.write( "   Use the rule used earlier to rewrite this equation as \r\n" );
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document.write( "      4/x = 10<sup>-1</sup>\r\n" );
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document.write( "   Use the rule A<sup>-B</sup> = 1/A<sup>B</sup> to rewrite the RHS\r\n" );
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document.write( "      4/x = 1/10<sup>1</sup>\r\n" );
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document.write( "      4/x = 1/10\r\n" );
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document.write( "   Multiply both sides by 10x\r\n" );
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document.write( "     10x·4/x = 10x·1/10\r\n" );
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document.write( "          40 = x   \r\n" );
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document.write( "6.  log(x + 21) + log(x) = 2\r\n" );
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document.write( "  Use the rule \r\n" );
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document.write( "    log(A) + log(B) = log(AB) to rewrite the LHS\r\n" );
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document.write( "        log[(x + 21)x] = 2\r\n" );
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document.write( "         log(x<sup>2</sup> + 21x) = 2\r\n" );
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document.write( "  Now use the first rule to rewrite that equation as\r\n" );
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document.write( "              x<sup>2</sup> + 21x = 10<sup>2</sup>\r\n" );
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document.write( "        x<sup>2</sup> + 21x - 100 = 0\r\n" );
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document.write( "       (x + 25)(x - 4) = 0\r\n" );
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document.write( "        x + 25 = 0;  x - 4 = 0\r\n" );
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document.write( "             x = -25;  x = 4\r\n" );
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document.write( "  We discard the negative answer because we cannot take logs \r\n" );
document.write( "  of negative numbers.\r\n" );
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document.write( "  The answer is x = 4  \r\n" );
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document.write( "Edwin\r\n" );
document.write( "AnlytcPhil@aol.com</PRE>          </SPAN>\n" );
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