document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=892606>Question 892606</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Solve 125^x=5 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #540624 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=540624\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> start with 125^x = 5\r<BR>\n" );
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document.write( "take the log of both sides of this equation to get:\r<BR>\n" );
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document.write( "log(125^x) = log(5)\r<BR>\n" );
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document.write( "since log(125^x) = x * log(125), your equation becomes:\r<BR>\n" );
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document.write( "x * log(125) = log(5)\r<BR>\n" );
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document.write( "divide both sides of this equation by log(125) to get:\r<BR>\n" );
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document.write( "x = log(5) / log(125)\r<BR>\n" );
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document.write( "use the log function of your calculator to get:\r<BR>\n" );
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document.write( "x = .3333333........\r<BR>\n" );
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document.write( "this is the same as x = 1/3\r<BR>\n" );
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document.write( "your original equation of 225^x = 5 becomes 225^(1/3) = x\r<BR>\n" );
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document.write( "since 225^(1/3) = the cube root of 125, your equation becomes:\r<BR>\n" );
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document.write( "cube root (125) = 5\r<BR>\n" );
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document.write( "since cube root (125) = 5 because 5^3 = 125, your equation becomes:\r<BR>\n" );
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document.write( "5 = 5\r<BR>\n" );
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document.write( "this confirms the solution is correct.<BR>\n" );
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