document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=678813>Question 678813</A>: <I><SPAN STYLE=\"word-break: break-all;\">  10^3x+1=100 what does x equal? <BR>\n" );
document.write( "x= ? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #421766 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=421766\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> First of all, is the equation<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=10%5E%283x%2B1%29+=+100 ALIGN=MIDDLE  ALT=\"10%5E%283x%2B1%29+=+100\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "or<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=10%5E3x%2B1+=+100 ALIGN=MIDDLE  ALT=\"10%5E3x%2B1+=+100\"   DISABLED_style= \"max-width:90%; height:auto;\" >?<BR>\n" );
document.write( "I think you meant the first one but what you entered meant the second one. If I'm right then please put parentheses around multiple-term exponents. If I'm wrong then the rest of this will not help because I will be solving the first one.<br><BR>\n" );
document.write( "Solving equations where the variable is in an exponent can be done with logarithms. However there is an easier solution if the equation can be rewritten so each side is a power of the same number. Your equation can be solved this way.<br><BR>\n" );
document.write( "The left side is already a power of 10. Can we rewrite the right side so that it is also a power of 10? Or can we rewrite both sides so that they are both powers of the same third number? The answer to the first question is yes:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=10%5E%283x%2B1%29+=+10%5E2 ALIGN=MIDDLE  ALT=\"10%5E%283x%2B1%29+=+10%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "The equation now says that two powers of 10 are equal. The only way this can be true is if the exponents are equal. So:<BR>\n" );
document.write( "3x+1 = 2<BR>\n" );
document.write( "This is simple to solve:<BR>\n" );
document.write( "3x = 1<BR>\n" );
document.write( "x = 1/3 </SPAN>\n" );
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