document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=169886>Question 169886</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Please help me solve this equation: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+2.79%5E%28x-1%29+-+4.377%5Ex+=+0+ ALIGN=MIDDLE  ALT=\"+2.79%5E%28x-1%29+-+4.377%5Ex+=+0+\"   DISABLED_style= \"max-width:90%; height:auto;\" >. Thank you! </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #125305 by </B><A HREF=/tutors/aboutme.mpl?userid=gonzo><B>gonzo(654)</B></A><img src=\"/images/stars/stars-11.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=gonzo><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=125305\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> problem:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+2.79%5E%28x-1%29+-+4.377%5Ex+=+0+ ALIGN=MIDDLE  ALT=\"+2.79%5E%28x-1%29+-+4.377%5Ex+=+0+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "-----<BR>\n" );
document.write( "not sure if this is the correct way to approach this, but i got a solution and it appears to be good.<BR>\n" );
document.write( "----- <BR>\n" );
document.write( "you start off with:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2.79%5E%28x-1%29+-+4.377%5Ex+=+0 ALIGN=MIDDLE  ALT=\"2.79%5E%28x-1%29+-+4.377%5Ex+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "add 4.377^x to both sides of the equation:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2.79%5E%28x-1%29+=+4.377%5Ex ALIGN=MIDDLE  ALT=\"2.79%5E%28x-1%29+=+4.377%5Ex\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "raise both sides of the equation to the <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%281%2F%28x-1%29%29 ALIGN=MIDDLE  ALT=\"%281%2F%28x-1%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > exponent.<BR>\n" );
document.write( "your equation becomes:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%282.79%5E%28x-1%29%29%5E%281%2F%28x-1%29%29+=+%284.377%5Ex%29%5E%281%2F%28x-1%29%29 ALIGN=MIDDLE  ALT=\"%282.79%5E%28x-1%29%29%5E%281%2F%28x-1%29%29+=+%284.377%5Ex%29%5E%281%2F%28x-1%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "simplify this and it becomes:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2.79%5E1+=+4.377%5E%28x%2F%28x-1%29%29 ALIGN=MIDDLE  ALT=\"2.79%5E1+=+4.377%5E%28x%2F%28x-1%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "which is the same as:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2.79+=+4.377%5E%28x%2F%28x-1%29%29 ALIGN=MIDDLE  ALT=\"2.79+=+4.377%5E%28x%2F%28x-1%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "-----<BR>\n" );
document.write( "now that you have this in a standard exponential form, you should be able to solve it using logarithms.<BR>\n" );
document.write( "you make use of two logarithmic formulas:<BR>\n" );
document.write( "first formula:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+a%5Ex ALIGN=MIDDLE  ALT=\"y+=+a%5Ex\"   DISABLED_style= \"max-width:90%; height:auto;\" > if and only if <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%28a%2Cy%29+=+x ALIGN=MIDDLE  ALT=\"log%28a%2Cy%29+=+x\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "second formula:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%28a%2Cy%29+=+log%2810%2Cy%29+%2F+log%2810%2Ca%29 ALIGN=MIDDLE  ALT=\"log%28a%2Cy%29+=+log%2810%2Cy%29+%2F+log%2810%2Ca%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "-----<BR>\n" );
document.write( "using the first formula, your formula of:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2.79+=+4.377%5E%28x%2F%28x-1%29%29 ALIGN=MIDDLE  ALT=\"2.79+=+4.377%5E%28x%2F%28x-1%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "becomes:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%284.377%2C2.79%29+=+x%2F%28x-1%29 ALIGN=MIDDLE  ALT=\"log%284.377%2C2.79%29+=+x%2F%28x-1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "----<BR>\n" );
document.write( "using the second formula,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%284.377%2C2.79%29+=+x%2F%28x-1%29 ALIGN=MIDDLE  ALT=\"log%284.377%2C2.79%29+=+x%2F%28x-1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "becomes:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28log%2810%2C2.79%29+%2F+log%2810%2C4.377%29%29+=+x%2F%28x-1%29 ALIGN=MIDDLE  ALT=\"%28log%2810%2C2.79%29+%2F+log%2810%2C4.377%29%29+=+x%2F%28x-1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "-----<BR>\n" );
document.write( "this becomes:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=.69497895+=+x%2F%28x-1%29 ALIGN=MIDDLE  ALT=\".69497895+=+x%2F%28x-1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "let the letter \"a\" represent \".69497895\" for now to make simplifying easier to show.<BR>\n" );
document.write( "equation becomes:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a+=+x%2F%28x-1%29 ALIGN=MIDDLE  ALT=\"a+=+x%2F%28x-1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "multiply both sides of equation by (x-1)<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%2A%28x-1%29+=+x ALIGN=MIDDLE  ALT=\"a%2A%28x-1%29+=+x\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "simplify:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%2Ax+-+a+=+x ALIGN=MIDDLE  ALT=\"a%2Ax+-+a+=+x\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "add a to both sides of equation and subtract x from both sides of equation:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%2Ax+-+x+=+a ALIGN=MIDDLE  ALT=\"a%2Ax+-+x+=+a\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "factor out the x:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2A%28a-1%29+=+a ALIGN=MIDDLE  ALT=\"x%2A%28a-1%29+=+a\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "divide both sides by (a-1)<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+a%2F%28a-1%29 ALIGN=MIDDLE  ALT=\"x+=+a%2F%28a-1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "replace a with .69497895 and solve\"<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+.69497895%2F%281-.69497895%29 ALIGN=MIDDLE  ALT=\"x+=+.69497895%2F%281-.69497895%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+.69497895%2F-.30502105 ALIGN=MIDDLE  ALT=\"x+=+.69497895%2F-.30502105\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=+-2.278462259 ALIGN=MIDDLE  ALT=\"x=+-2.278462259\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "-----<BR>\n" );
document.write( "plug that value of x into your original equation:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2.79%5E%28x-1%29+-+4.377%5Ex+=+0 ALIGN=MIDDLE  ALT=\"2.79%5E%28x-1%29+-+4.377%5Ex+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "becomes:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2.79%5E%28-3.278462259%29+-+4.377%5E%28-2.278462259%29+=+0 ALIGN=MIDDLE  ALT=\"2.79%5E%28-3.278462259%29+-+4.377%5E%28-2.278462259%29+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "you will find the answer to be 0 proving the value of x is correct.<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "i may have messed up the digits but the real values were stored in the calculator and are accurate.<BR>\n" );
document.write( "the values should be:<BR>\n" );
document.write( ".69497895 for a<BR>\n" );
document.write( "-.30502105 for 1-a<BR>\n" );
document.write( "-2.278462259 for x<BR>\n" );
document.write( "any deviation from these numbers above is a typo.<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "there might be an easier way to do this but i don't see it right now.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );