document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=434121>Question 434121</A>: <I><SPAN STYLE=\"word-break: break-all;\"> please help me solve this problem using logarithms: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+5%282%5EX%29+=+3+-+2%5E%28x%2B2%29+ ALIGN=MIDDLE  ALT=\"+5%282%5EX%29+=+3+-+2%5E%28x%2B2%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #300844 by </B><A HREF=/tutors/aboutme.mpl?userid=Gogonati><B>Gogonati(855)</B></A><img src=\"/images/stars/stars-11.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Gogonati><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=Gogonati><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=300844\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> To solve the equation:<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5%2A2%5Ex=3-2%5E%28x%2B2%29 ALIGN=MIDDLE  ALT=\"5%2A2%5Ex=3-2%5E%28x%2B2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >, we substitute <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%5Ex=y ALIGN=MIDDLE  ALT=\"2%5Ex=y\"   DISABLED_style= \"max-width:90%; height:auto;\" > and\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%5E%28x%2B2%29=2%5E2%2A2%5Ex=4%2Ay ALIGN=MIDDLE  ALT=\"2%5E%28x%2B2%29=2%5E2%2A2%5Ex=4%2Ay\"   DISABLED_style= \"max-width:90%; height:auto;\" >. Rewrite the equation: 5y=3-4y, solve this equation,\r<BR>\n" );
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document.write( "5y+4y=3 => 9y=3 => y=1/3. Now we find the x, since 2^x=y, substitute:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%5Ex=1%2F3 ALIGN=MIDDLE  ALT=\"2%5Ex=1%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" >, taking natural logarithms of each side we have:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2Aln2=-ln3 ALIGN=MIDDLE  ALT=\"x%2Aln2=-ln3\"   DISABLED_style= \"max-width:90%; height:auto;\" > => <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=-ln3%2Fln2 ALIGN=MIDDLE  ALT=\"x=-ln3%2Fln2\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "Done.\r<BR>\n" );
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