document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=354347>Question 354347</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Solve. Round to four decimal places\r<BR>\n" );
document.write( "\n" );
document.write( "a) e^3x >_ 21\r<BR>\n" );
document.write( "\n" );
document.write( "b) (1/5)^t-2 = 125 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #253774 by </B><A HREF=/tutors/aboutme.mpl?userid=jsmallt9><B>jsmallt9(3758)</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=253774\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> a) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=e%5E%283x%29+%3E=+21 ALIGN=MIDDLE  ALT=\"e%5E%283x%29+%3E=+21\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Find the natural log (because of the \"e\" and because we want a decimal):<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=ln%28e%5E%283x%29%29+%3E=+21 ALIGN=MIDDLE  ALT=\"ln%28e%5E%283x%29%29+%3E=+21\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Use a property of logarithms, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%28a%2C+%28p%5Eq%29%29+=+q%2Alog%28a%2C+%28p%29%29 ALIGN=MIDDLE  ALT=\"log%28a%2C+%28p%5Eq%29%29+=+q%2Alog%28a%2C+%28p%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >, to move the exponent out in front:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3x%2Aln%28e%29+%3E=+21 ALIGN=MIDDLE  ALT=\"3x%2Aln%28e%29+%3E=+21\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "By definition, ln(e) = 1 so this simplifies to:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3x+%3E=+21 ALIGN=MIDDLE  ALT=\"3x+%3E=+21\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Divide both sides by 3:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+%3E=+21 ALIGN=MIDDLE  ALT=\"x+%3E=+21\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "b) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%281%2F5%29%5E%28t-2%29+=+125 ALIGN=MIDDLE  ALT=\"%281%2F5%29%5E%28t-2%29+=+125\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "The quick way to solve this comes from recognizing that both sides are powers of 5: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F5+=+5%5E%28-1%29 ALIGN=MIDDLE  ALT=\"1%2F5+=+5%5E%28-1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=125+=+5%5E3 ALIGN=MIDDLE  ALT=\"125+=+5%5E3\"   DISABLED_style= \"max-width:90%; height:auto;\" >. Subsituting these in we get:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%285%5E%28-1%29%29%5E%28t-2%29%29+=+5%5E3 ALIGN=MIDDLE  ALT=\"%285%5E%28-1%29%29%5E%28t-2%29%29+=+5%5E3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "On the left side the rule is to multiply exponents:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5%5E%28-t%2B2%29+=+5%5E3 ALIGN=MIDDLE  ALT=\"5%5E%28-t%2B2%29+=+5%5E3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Now the equation explicitly says each side is a power of 5. And if these two powers of 5 are equal, then the exponents must be equal!<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-t+%2B+2+=+3 ALIGN=MIDDLE  ALT=\"-t+%2B+2+=+3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Solving this:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-t+=+1 ALIGN=MIDDLE  ALT=\"-t+=+1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t+=+-1 ALIGN=MIDDLE  ALT=\"t+=+-1\"   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );