document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1016251>Question 1016251</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Hi,<BR>\n" );
document.write( "I'm unsure on how to solve this problem:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+7%5E%282x%29+=+49%5E%283x%2B1%29+ ALIGN=MIDDLE  ALT=\"+7%5E%282x%29+=+49%5E%283x%2B1%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Thank you so much to anyone who can help! </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #632684 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=632684\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> 7^(2x) = 49^(3x+1)\r<BR>\n" );
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document.write( "one way to solve this is:\r<BR>\n" );
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document.write( "start with:\r<BR>\n" );
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document.write( "7^(2x) = 49^(3x+1)\r<BR>\n" );
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document.write( "since 49 = 7^2, this equation becomes:\r<BR>\n" );
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document.write( "7^(2x) = (7^2)^(3x+1)\r<BR>\n" );
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document.write( "this becomes 7^(2x) = 7^(2*(3x+1)) which becomes:\r<BR>\n" );
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document.write( "7^(2x) = 7^(6x + 2)\r<BR>\n" );
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document.write( "since the base is the same, you can just set the exponents equal to each other and solve for x.\r<BR>\n" );
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document.write( "you get 2x = 6x + 2\r<BR>\n" );
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document.write( "solve for x to get x = -1/2\r<BR>\n" );
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document.write( "another way to solve it is:\r<BR>\n" );
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document.write( "start with:\r<BR>\n" );
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document.write( "7^(2x) = 49^(3x+1)\r<BR>\n" );
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document.write( "take the log of both sides of the equation to get:\r<BR>\n" );
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document.write( "log(7^(2x) = log(49^(3x+1))\r<BR>\n" );
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document.write( "this becomes 2x * log(7) = (3x+1) * log(49)\r<BR>\n" );
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document.write( "since 49 is equal to 7^2, this becomes 2x * log(7) = (3x+1) * log(7^2).\r<BR>\n" );
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document.write( "this becomes 2x * log(7) = 2 * (3x + 1) * log(7) which becomes:\r<BR>\n" );
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document.write( "2x * log(7) = (6x + 2) * log(7)\r<BR>\n" );
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document.write( "if  you divide both sides of this equation by log(7), you get:\r<BR>\n" );
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document.write( "2x = 6x + 2\r<BR>\n" );
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document.write( "solve for x to get x = -1/2\r<BR>\n" );
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document.write( "if you did not recognize that 49 = 7^2 and that you could then get 2 * log(7), you could still have solved as follows:\r<BR>\n" );
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document.write( "start with:\r<BR>\n" );
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document.write( "2x * log(7) = (3x+1) * log(49)\r<BR>\n" );
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document.write( "find log(7) and find log(49) and the equation becomes:\r<BR>\n" );
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document.write( "2x * .84509804 = (3x + 1) * 1.69019608\r<BR>\n" );
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document.write( "simplify to get:\r<BR>\n" );
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document.write( "1.69019608 * x = 3x * 1.69019608 + 1 * 1.69019608\r<BR>\n" );
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document.write( "this becomes 1.69019608 * x = 5.07058824 * x + 1.69019608\r<BR>\n" );
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document.write( "subtract 1.69019608 * x from both sides of the equation and subtract 1.69019608 from both sides of the equation to get:\r<BR>\n" );
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document.write( "-1.69019608 = 5.07058824 * x - 1.69019608 * x\r<BR>\n" );
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document.write( "combine like terms to get -1.69019608 = 3.38039216 * x\r<BR>\n" );
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document.write( "divide both sides of this equation by 3.38039216 and solve for x to get:\r<BR>\n" );
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document.write( "x = 3.38039216 / -1.69019608 = -.5 which is the same as -1/2.\r<BR>\n" );
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document.write( "it was a lot messier because of the arithmetic involved but you go the same answer.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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