document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=664119>Question 664119</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Im having trouble solving Log base 3 of 27^-1 = x. i know to move the -1 in front of log and make it -1(log base 3 of 27)=x, but now im stuck. Can someone please help? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #413136 by </B><A HREF=/tutors/aboutme.mpl?userid=Theo><B>Theo(13342)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Theo><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=Theo><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=413136\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> log3(27^-1) = x\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "one way to solve this is shown below:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "log3(27^-1) = x if and only if 3^x = 27^-1<BR>\n" );
document.write( "take the log10 of both sides of this equation to get:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "log10(3^x) = log10(27^-1)<BR>\n" );
document.write( "since log10 is the LOG function of your calculator, this equation becomes:<BR>\n" );
document.write( "LOG(3^x) = LOG(27^-1)\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "since,in general, log(a^b) = b*log(a), then this equation becomes:<BR>\n" );
document.write( "x*LOG(3) = -1*LOG(27)<BR>\n" );
document.write( "divide both sides of this equation to get:<BR>\n" );
document.write( "x = -1*LOG(27)/LOG(3)<BR>\n" );
document.write( "solve for x using your calculator to get:<BR>\n" );
document.write( "x = -3\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "that's your answer.,\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "confirm by replacing x in your original equation with -3<BR>\n" );
document.write( "you get:<BR>\n" );
document.write( "log3(27^-1) = -3\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "you can convert log3 to log10 by using the log base conversion formula.<BR>\n" );
document.write( "that formula is:<BR>\n" );
document.write( "log3(27^-1) = log10(27^-1)/log10(3)<BR>\n" );
document.write( "since log10 is equal to the LOG function of your calculator, this becomes:<BR>\n" );
document.write( "log3(27^-1) = LOG(27^-1)/LOG(3)<BR>\n" );
document.write( "use your calculator to solve this to get:<BR>\n" );
document.write( "log3(27^-1) = -3\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );