document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=886287>Question 886287</A>: <I><SPAN STYLE=\"word-break: break-all;\"> 2e^(x+3) = &#960;^x </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #535883 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=535883\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> 2*e^(x+3) = pi^x\r<BR>\n" );
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document.write( "divide both sides of this equation by 2 to get:\r<BR>\n" );
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document.write( "e^(x+3) = pi^x/2\r<BR>\n" );
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document.write( "take natural log of both sides of this equation to get:\r<BR>\n" );
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document.write( "ln(e^(x+3) = ln(pi^x/2)\r<BR>\n" );
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document.write( "since log(a^b) = b*log(a) and log(a*b) = log(a) + log(b), your equation becomes:\r<BR>\n" );
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document.write( "(x+3)*ln(e) = ln(pi^x) = ln(2)\r<BR>\n" );
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document.write( "since ln(e) = 1 and log(a^b) = b*log(a), your equation becomes:\r<BR>\n" );
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document.write( "(x+3) = x * ln(pi) - ln(2)\r<BR>\n" );
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document.write( "add ln(2) to both sides of this equation and subtract (x+3) from both sides of this equation to get:\r<BR>\n" );
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document.write( "ln(2) = x * ln(pi) - (x+3)\r<BR>\n" );
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document.write( "simplify this to get:\r<BR>\n" );
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document.write( "ln(2) = x*ln(pi) - x - 3\r<BR>\n" );
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document.write( "factor out the x to get:\r<BR>\n" );
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document.write( "ln(2) = x * (ln(pi) - 1) - 3\r<BR>\n" );
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document.write( "add 3 to both sides of the equation to get:\r<BR>\n" );
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document.write( "ln(2) + 3 = x * (ln(pi) - 1)\r<BR>\n" );
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document.write( "divide both sides of the equation by (ln(pi) - 1) to get:\r<BR>\n" );
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document.write( "(ln(2) + 3) / (ln(pi) - 1) = x\r<BR>\n" );
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document.write( "that's your solution.\r<BR>\n" );
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document.write( "to confirm the solution is correct, replace x in your original equation with the value of x in the solution to see if the equation holds true.\r<BR>\n" );
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document.write( "decimal equivalent of x = 25.51751602\r<BR>\n" );
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document.write( "after replacing x with 25.51751602, I got:\r<BR>\n" );
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document.write( "2*e^(x+3) = pi^x becomes:\r<BR>\n" );
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document.write( "4.853218453 * 10^12 = 4.853218453 * 10^12\r<BR>\n" );
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document.write( "this confirms the solution is correct.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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