document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=38907>Question 38907</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Hello,\r<BR>\n" );
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document.write( "I need help with a few problems i cant seem to work out for homework.  \r<BR>\n" );
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document.write( "1:Solve for x: 9^x=3<BR>\n" );
document.write( "2:Solve for x: 2^9x^-4=32<BR>\n" );
document.write( "3:Solve for x: log10^7=log10x-log10^2\r<BR>\n" );
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document.write( "Thanks  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #24373 by </B><A HREF=/tutors/aboutme.mpl?userid=AnlytcPhil><B>AnlytcPhil(1806)</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=24373\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Hello, <BR>\n" );
document.write( "I need help with a few problems i cant seem to work out for homework. <BR>\n" );
document.write( "1:Solve for x: 9^x=3<BR>\n" );
document.write( "2:Solve for x: 2^9x^-4=32<BR>\n" );
document.write( "3:Solve for x: log10^7=log10x-log10^2 <BR>\n" );
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document.write( "9<sup>x</sup> = 3\r\n" );
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document.write( "We can relate the two numbers 3 and 9 by the equation\r\n" );
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document.write( "9 = 3<sup>2</sup>\r\n" );
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document.write( "So we substitute (32) for 9\r\n" );
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document.write( "(3<sup>2</sup>)<sup>x</sup> = 3\r\n" );
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document.write( "Remove the parentheses by multiplying outer \r\n" );
document.write( "exponent x by inner exponent 2\r\n" );
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document.write( "3<sup>2x</sup> = 3\r\n" );
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document.write( "Now write the 3 on the right as 31\r\n" );
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document.write( "3<sup>2x</sup> = 3<sup>1</sup>\r\n" );
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document.write( "Now use the fact that if two exponential expressions are equal\r\n" );
document.write( "and the common base is positive and not 1, then the exponents are\r\n" );
document.write( "equal, so we equate the exponents of 3 on both sides:\r\n" );
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document.write( "2x = 1\r\n" );
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document.write( " x = 1/2\r\n" );
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document.write( "2^9x^-4=32\r\n" );
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document.write( "Big problem here! I can't tell if that means\r\n" );
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document.write( "(A)   2<sup>9</sup>x<sup>-4</sup> = 32\r\n" );
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document.write( "or\r\n" );
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document.write( "(B)   2<sup>9x<sup>-4</sup></sup> = 32\r\n" );
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document.write( "or\r\n" );
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document.write( "(C)   (2<sup>9x</sup>)<sup>-4</sup> = 32\r\n" );
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document.write( "If it means (A)\r\n" );
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document.write( "2<sup>9</sup>x<sup>-4</sup> = 32\r\n" );
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document.write( "Substitute 2<sup>5</sup> for 32\r\n" );
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document.write( "2<sup>9</sup>x<sup>-4</sup> = 2<sup>5</sup>\r\n" );
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document.write( "Divide both sides by 2<sup>9</sup>\r\n" );
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document.write( "    x<sup>-4</sup> = 2<sup>5</sup>/2<sup>9</sup>\r\n" );
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document.write( "    x<sup>-4</sup> = 2<sup>-4</sup>\r\n" );
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document.write( "Raise both sides to the -1/4 power\r\n" );
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document.write( "    (x<sup>-4</sup>)<sup>-1/4</sup> = (2<sup>-4</sup>)<sup>-1/4</sup>\r\n" );
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document.write( "        x<sup>1</sup> = 2<sup>1</sup>        \r\n" );
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document.write( "         x = 2                       \r\n" );
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document.write( "If it means (B)\r\n" );
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document.write( "(B)   2<sup>9x<sup>-4</sup></sup> = 32\r\n" );
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document.write( "Substitute 2<sup>5</sup> for 32\r\n" );
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document.write( "  2<sup>9x<sup>-4</sup></sup> = 2<sup>5</sup>\r\n" );
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document.write( "Now use the fact that if two exponential expressions are equal\r\n" );
document.write( "and the common base is positive and not 1, then the exponents are\r\n" );
document.write( "equal, so we equate the exponents of 2 on both sides:\r\n" );
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document.write( "    9x<sup>-4</sup> = 5\r\n" );
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document.write( "Divide both sides by 9\r\n" );
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document.write( "     x<sup>-4</sup> = 5/9   \r\n" );
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document.write( "Raise both sides to the -1/4 power\r\n" );
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document.write( "    (x-4)<sup>-1/4</sup> = (5/9)<sup>-1/4</sup>\r\n" );
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document.write( "     x<sup>1</sup> = (9/5)<sup>1/4</sup>\r\n" );
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document.write( "      x = (9/5)<sup>1/4</sup>\r\n" );
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document.write( "      x = 1.158292185 approximately\r\n" );
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document.write( "If it means (C)\r\n" );
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document.write( "(2<sup>9x</sup>)<sup>-4</sup> = 32\r\n" );
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document.write( "Remove the parentheses on the left by \r\n" );
document.write( "multiplying the outer exponent -4 by the\r\n" );
document.write( "inner exponent 9x. On the right, substitute\r\n" );
document.write( "2<sup>5</sup> for 32\r\n" );
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document.write( "2<sup>-36x</sup> = 2<sup>5</sup>\r\n" );
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document.write( "Now use the fact that if two exponential expressions are equal\r\n" );
document.write( "and the common base is positive and not 1, then the exponents are\r\n" );
document.write( "equal, so we equate the exponents of 2 on both sides:\r\n" );
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document.write( "-36x = 5\r\n" );
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document.write( "  x = -5/36\r\n" );
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document.write( "log(10<sup>7</sup>) = log(10x) - log(10<sup>2</sup>)\r\n" );
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document.write( "Use fact that log(10<sup>N</sup>) = N\r\n" );
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document.write( "     7 = log(10x) - 2\r\n" );
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document.write( "     9 = log(10x)\r\n" );
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document.write( "Use the fact that log(AB) = log(A) + log(B)\r\n" );
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document.write( "     9 = log(10) + log(x)\r\n" );
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document.write( "Use the fact that log(10) = log(10<sup>1</sup>) = 1\r\n" );
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document.write( "     9 = 1 + log(x)\r\n" );
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document.write( "     8 = log(x)\r\n" );
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document.write( "Use the fact that equation A = log(B) can be written\r\n" );
document.write( "as equation B = 10<sup>A</sup> \r\n" );
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document.write( "    x = 10<sup>8</sup>\r\n" );
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document.write( "    x = 100,000,000    \r\n" );
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document.write( "Edwin\r\n" );
document.write( "AnlytcPhil@aol.com</PRE></font><BR>\n" );
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