document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=202239>Question 202239</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Solve for x: log(subscript5)(x)=-2. thanks. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #152503 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=152503\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> this says:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%285%2Cx%29+=+-2 ALIGN=MIDDLE  ALT=\"log%285%2Cx%29+=+-2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "because logarithms are inverse of exponents, this formula can only be true if and only if...<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5%5E%28-2%29+=+x ALIGN=MIDDLE  ALT=\"5%5E%28-2%29+=+x\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "which should be the same as:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F5%5E2+=+x+ ALIGN=MIDDLE  ALT=\"1%2F5%5E2+=+x+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "since <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5%5E2 ALIGN=MIDDLE  ALT=\"5%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 25, this becomes:<BR>\n" );
document.write( "(1/25) = x<BR>\n" );
document.write( "The answer should be (1/25)<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "to prove this is true, substitute (1/25) for x and solve.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%285%2C%281%2F25%29%29+=+-2+ ALIGN=MIDDLE  ALT=\"log%285%2C%281%2F25%29%29+=+-2+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "is the same as:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%285%2C1%29+-+log%285%2C25%29+=+-2 ALIGN=MIDDLE  ALT=\"log%285%2C1%29+-+log%285%2C25%29+=+-2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "to solve using your calculator, you can convert the base 5 to the base 10 or to the natural log base.<BR>\n" );
document.write( "let's try the base 10.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%285%2C1%29+=+log%2810%2C1%29%2Flog%2810%2C5%29+ ALIGN=MIDDLE  ALT=\"log%285%2C1%29+=+log%2810%2C1%29%2Flog%2810%2C5%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 0/.698..... = 0<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%285%2C25%29+=+log%2810%2C25%29+%2F+log%2810%2C5%29+ ALIGN=MIDDLE  ALT=\"log%285%2C25%29+=+log%2810%2C25%29+%2F+log%2810%2C5%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 2<BR>\n" );
document.write( "so...<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%285%2C%281%2F25%29%29+=+log%285%2C1%29+-+log%285%2C15%29+=+-2+ ALIGN=MIDDLE  ALT=\"log%285%2C%281%2F25%29%29+=+log%285%2C1%29+-+log%285%2C15%29+=+-2+\"   DISABLED_style= \"max-width:90%; height:auto;\" > which is true,<BR>\n" );
document.write( "so x = (1/25) is a good answer.<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "another way to prove it is to convert back to exponents by taking the inverse.<BR>\n" );
document.write( "we start off with:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%285%2C%281%2F25%29%29+=+-2 ALIGN=MIDDLE  ALT=\"log%285%2C%281%2F25%29%29+=+-2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "this is true if and only if:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5%5E%28-2%29+=+%281%2F25%29+ ALIGN=MIDDLE  ALT=\"5%5E%28-2%29+=+%281%2F25%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "we'll cheat this time by using the calculator.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5%5E%28-2%29+=+.04+ ALIGN=MIDDLE  ALT=\"5%5E%28-2%29+=+.04+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ".04 is the same as .04/1<BR>\n" );
document.write( "multiply numerator and denominator by 25 (doesn't change the fraction), and we get<BR>\n" );
document.write( "(.04*25)/(1*25) = (1/25), which is the answer we are looking for.<BR>\n" );
document.write( "bottom line:<BR>\n" );
document.write( "x = (1/25)<BR>\n" );
document.write( "----- </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );