document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1057131>Question 1057131</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I just need someone to explain this and why 2 is the answer:<BR>\n" );
document.write( "3^(log base 9 (4))= 2\r<BR>\n" );
document.write( "\n" );
document.write( "I'm not sure how to write out log base correctly, but it's log(4) with the base of 9. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #672220 by </B><A HREF=/tutors/aboutme.mpl?userid=ikleyn><B>ikleyn(52798)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=ikleyn><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=ikleyn><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=672220\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> .<BR>\n" );
document.write( "I just need someone to explain this and why 2 is the answer:<BR>\n" );
document.write( "3^(log base 9 (4))= 2\r<BR>\n" );
document.write( "\n" );
document.write( "I'm not sure how to write out log base correctly, but it's log(4) with the base of 9.<BR>\n" );
document.write( "~~~~~~~~~~~~~~~~~~~~~~~\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "The problem is solved in two steps:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<PRE STYLE=\"white-space: pre-wrap; white-space: -moz-pre-wrap; white-space: -pre-wrap; white-space: -o-pre-wrap; word-wrap: break-word;\">\r\n" );
document.write( "1.  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%289%2C%284%29%29 ALIGN=MIDDLE  ALT=\"log%289%2C%284%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%283%2C%282%29%29 ALIGN=MIDDLE  ALT=\"log%283%2C%282%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "    Indeed, if <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%283%2C%282%29%29 ALIGN=MIDDLE  ALT=\"log%283%2C%282%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = x, it means (by the definition of logarithm) that <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3%5Ex ALIGN=MIDDLE  ALT=\"3%5Ex\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 2.\r\n" );
document.write( "    Then  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%283%5Ex%29%5E2 ALIGN=MIDDLE  ALT=\"%283%5Ex%29%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%5E2 ALIGN=MIDDLE  ALT=\"2%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 4, which implies  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3%5E%282x%29 ALIGN=MIDDLE  ALT=\"3%5E%282x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 4, which is the same as <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%283%5E2%29%5Ex ALIGN=MIDDLE  ALT=\"%283%5E2%29%5Ex\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 4,  or  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=9%5Ex ALIGN=MIDDLE  ALT=\"9%5Ex\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 4.\r\n" );
document.write( "    The last equality means that <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%289%2C%284%29%29 ALIGN=MIDDLE  ALT=\"log%289%2C%284%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = x.  Hence,  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%289%2C%284%29%29 ALIGN=MIDDLE  ALT=\"log%289%2C%284%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%283%2C%282%29%29 ALIGN=MIDDLE  ALT=\"log%283%2C%282%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >,  QED.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "2.  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3%5E%28log%283%2C%282%29%29%29 ALIGN=MIDDLE  ALT=\"3%5E%28log%283%2C%282%29%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 2.    (<---- <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b%5E%28log%28b%2C%28x%29%29%29 ALIGN=MIDDLE  ALT=\"b%5E%28log%28b%2C%28x%29%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = x  for any x > 0 and for any b > 0,  b=/= 1.  \r\n" );
document.write( "                                 This is the basic property of the logarithm, equivalent to the definition of the logarithm)\r\n" );
document.write( "</PRE>\r<BR>\n" );
document.write( "\n" );
document.write( "On logarithms, see the lessons\r<BR>\n" );
document.write( "\n" );
document.write( "&nbsp;&nbsp;&nbsp;&nbsp;- <A  rel=nofollow HREF=http://www.algebra.com/algebra/homework/logarithm/what-is-the-logarithm.lesson>WHAT IS the logarithm</A>  \r<BR>\n" );
document.write( "\n" );
document.write( "&nbsp;&nbsp;&nbsp;&nbsp;- <A  rel=nofollow HREF=http://www.algebra.com/algebra/homework/logarithm/Properties-of-the-logarithm.lesson>Properties of the logarithm</A>  \r<BR>\n" );
document.write( "\n" );
document.write( "in this site.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Also, you have this free of charge online textbook in ALGEBRA-I in this site\r<BR>\n" );
document.write( "\n" );
document.write( "&nbsp;&nbsp;&nbsp;&nbsp;- <A  rel=nofollow HREF=https://www.algebra.com/algebra/homework/quadratic/lessons/ALGEBRA-I-YOUR-ONLINE-TEXTBOOK.lesson>ALGEBRA-I - YOUR ONLINE TEXTBOOK</A>.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "The referred lessons are the part of this online textbook under the topic \"<U>Logarithms</U>\".\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );