document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1197628>Question 1197628</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Rewrite the equation in terms of base e. Express the answer in terms of a natural logarithm and then round to three decimal places.<BR>\n" );
document.write( "y=101(4.8)x\r<BR>\n" );
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document.write( "Part 1<BR>\n" );
document.write( "Express the answer in terms of a natural logarithm.<BR>\n" );
document.write( "y=_________<BR>\n" );
document.write( "Part 2:<BR>\n" );
document.write( "Simplify the​ answer, rounding to three decimal places.<BR>\n" );
document.write( "y=________ </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #830989 by </B><A HREF=/tutors/aboutme.mpl?userid=MathLover1><B>MathLover1(20850)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=MathLover1><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=MathLover1><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=830989\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> \r<BR>\n" );
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document.write( "Part 1\r<BR>\n" );
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document.write( "Express the answer in terms of a natural logarithm.\r<BR>\n" );
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document.write( "Exponential expressions with natural base e are of the form <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+a%2Ae%5E%28kx%29 ALIGN=MIDDLE  ALT=\"y+=+a%2Ae%5E%28kx%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >. The value of 'a' is already set to be 3.4 since this is the coefficient of the given equation. We just need to find k\r<BR>\n" );
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document.write( "So set <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%280.4%29%5Ex ALIGN=MIDDLE  ALT=\"%280.4%29%5Ex\"   DISABLED_style= \"max-width:90%; height:auto;\" > equal to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=e%5E%28kx%29 ALIGN=MIDDLE  ALT=\"e%5E%28kx%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > and solve for k\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%284.8%29%5Ex+=+e%5E%28kx%29 ALIGN=MIDDLE  ALT=\"%284.8%29%5Ex+=+e%5E%28kx%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%284.8%29%5Ex+=+%28e%5Ek%29%5Ex ALIGN=MIDDLE  ALT=\"%284.8%29%5Ex+=+%28e%5Ek%29%5Ex\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4.8+=+e%5Ek ALIGN=MIDDLE  ALT=\"4.8+=+e%5Ek\"   DISABLED_style= \"max-width:90%; height:auto;\" > The two sides have the same exponent of x. So the two bases are 4.8 and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=e%5Ek ALIGN=MIDDLE  ALT=\"e%5Ek\"   DISABLED_style= \"max-width:90%; height:auto;\" > must be equal.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=ln%284.8%29+=+k ALIGN=MIDDLE  ALT=\"ln%284.8%29+=+k\"   DISABLED_style= \"max-width:90%; height:auto;\" > Convert to logarithmic form\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=k+=+ln%284.8%29 ALIGN=MIDDLE  ALT=\"k+=+ln%284.8%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+101%2Ae%5E%28ln%284.8%29x%29 ALIGN=MIDDLE  ALT=\"y+=+101%2Ae%5E%28ln%284.8%29x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Part 2:\r<BR>\n" );
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document.write( "Simplify the​ answer, rounding to three decimal places.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+101%2Ae%5E%28ln%284.8%29x%29 ALIGN=MIDDLE  ALT=\"y+=+101%2Ae%5E%28ln%284.8%29x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >..............<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=ln%284.8%29=1.5686159179138452=1.569 ALIGN=MIDDLE  ALT=\"ln%284.8%29=1.5686159179138452=1.569\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+101%2Ae%5E%281.569x%29 ALIGN=MIDDLE  ALT=\"y+=+101%2Ae%5E%281.569x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( " </SPAN>\n" );
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