document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=220562>Question 220562</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Could you please explain to me the process to solve the equations for x\r<BR>\n" );
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document.write( "1.3e^2x=28\r<BR>\n" );
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document.write( "2.2ln(x-5)=3.65 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #165653 by </B><A HREF=/tutors/aboutme.mpl?userid=jsmallt9><B>jsmallt9(3759)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=jsmallt9><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=165653\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> These problems require that we know how to convert from exponential form to logarithmic form and vice versa. So we we need to know:<ul><li><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%28a%2C+b%29+=+c ALIGN=MIDDLE  ALT=\"log%28a%2C+b%29+=+c\"   DISABLED_style= \"max-width:90%; height:auto;\" > in exponential form is: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5Ec+=+b ALIGN=MIDDLE  ALT=\"a%5Ec+=+b\"   DISABLED_style= \"max-width:90%; height:auto;\" ></li><li><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5Eb+=+c ALIGN=MIDDLE  ALT=\"a%5Eb+=+c\"   DISABLED_style= \"max-width:90%; height:auto;\" > in logarithmic form is: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%28a%2C+c%29+=+b ALIGN=MIDDLE  ALT=\"log%28a%2C+c%29+=+b\"   DISABLED_style= \"max-width:90%; height:auto;\" ></li></ul><BR>\n" );
document.write( "We also need to understand that <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=ln%28x%29 ALIGN=MIDDLE  ALT=\"ln%28x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > is the common name for <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%28e%2C+%28x%29%29 ALIGN=MIDDLE  ALT=\"log%28e%2C+%28x%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "Now we're ready to start:<BR>\n" );
document.write( "1. <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3e%5E%282x%29+=+28 ALIGN=MIDDLE  ALT=\"3e%5E%282x%29+=+28\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Whenever we solve for x we are trying to isolate x on one side of the equation. So we'll start by dividing by 3:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=e%5E%282x%29+=+28%2F3 ALIGN=MIDDLE  ALT=\"e%5E%282x%29+=+28%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Now we need to get x out of the exponent. This is where we need to know that this is the time to convert ro logarithmic form:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%28e%2C+%2828%2F3%29%29+=+2x ALIGN=MIDDLE  ALT=\"log%28e%2C+%2828%2F3%29%29+=+2x\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=ln%2828%2F3%29+=++2x ALIGN=MIDDLE  ALT=\"ln%2828%2F3%29+=++2x\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Now we can divide by 2:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28ln%2828%2F3%29%29%2F2+=++x ALIGN=MIDDLE  ALT=\"%28ln%2828%2F3%29%29%2F2+=++x\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "With a calculator we san simplify the left side:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1.1167961107535471+=+x ALIGN=MIDDLE  ALT=\"1.1167961107535471+=+x\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "2. <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2ln%28x-5%29=3.65%0D%0ADivide+by+2%3A%0D%0A%7B%7B%7Bln%28%28x-5%29%29=+1.825 ALIGN=MIDDLE  ALT=\"2ln%28x-5%29=3.65%0D%0ADivide+by+2%3A%0D%0A%7B%7B%7Bln%28%28x-5%29%29=+1.825\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Now we need to get x out of the argument of the logarithm. This is the time to convert to exponential form:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=e%5E1.825+=+x-5 ALIGN=MIDDLE  ALT=\"e%5E1.825+=+x-5\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Adding 5 to each side:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=e%5E1.825+%2B+5+=+x ALIGN=MIDDLE  ALT=\"e%5E1.825+%2B+5+=+x\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "With a calculator we can simplify the left side:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=11.2027950191048646+=+x ALIGN=MIDDLE  ALT=\"11.2027950191048646+=+x\"   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
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