document.write( "Question 49211: 5^2x-1=27.6\r
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Algebra.Com's Answer #32631 by AnlytcPhil(1807)\"\" \"About 
You can put this solution on YOUR website!
5^2x-1=27.6\r\n" );
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document.write( "solve for x\r\n" );
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document.write( "Thank you, Michelle\r\n" );
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document.write( "I think you mean\r\n" );
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document.write( "52x-1 = 27.6\r\n" );
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document.write( "Take natural logs of both sides:\r\n" );
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document.write( "ln(52x-1) = ln(27.6)\r\n" );
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document.write( "Now use the rule ln(MN) = N·ln(M) on the left side:\r\n" );
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document.write( "(2x - 1)ln(5) = ln(27.6)\r\n" );
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document.write( "Let A = ln(5) and B = ln(27.6)\r\n" );
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document.write( "(If you have a TI graphing calculator,\r\n" );
document.write( "a good idea here would be to store these\r\n" );
document.write( "two logs as A and B)\r\n" );
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document.write( "    (2x-1)A = B\r\n" );
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document.write( "    A(2x-1) = B\r\n" );
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document.write( "    2Ax - A = B\r\n" );
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document.write( "        2Ax = B + A\r\n" );
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document.write( "Divide both sides by 2A\r\n" );
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document.write( "          x = (B + A)/(2A)\r\n" );
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document.write( "Now replace A by ln(5) and B by ln(27.6)\r\n" );
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document.write( "  x = [ln(27.6) + ln(5)]/[2·ln(5)]\r\n" );
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document.write( "  x =  1.530737423\r\n" );
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document.write( "----------------------\r\n" );
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document.write( "Note: If the A and B above confuses you, \r\n" );
document.write( "then go back to this step:\r\n" );
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document.write( "             (2x - 1)ln(5) = ln(27.6)\r\n" );
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document.write( "find the logs on the calculator, and substitute:\r\n" );
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document.write( "     (2x - 1)(1.609437912) = 3.317815773\r\n" );
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document.write( "       1.609437912(2x - 1) = 3.317815773\r\n" );
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document.write( "3.218875825x - 1.609437912 = 3.317815773 \r\n" );
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document.write( "Add 1.609437912 to both sides:\r\n" );
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document.write( "              3.218875825x = 3.317815773 + 1.609437912 \r\n" );
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document.write( "              3.218875825x = 4.927253685\r\n" );
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document.write( "Divide both sides by coefficient 3.218875825\r\n" );
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document.write( "                         x = 4.927253685/3.218875825\r\n" );
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document.write( "                         x = 1.530737423\r\n" );
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document.write( "Edwin
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