document.write( "Question 233595: I am really struggling to find the answer to this logarithmic equation that we have been set:\r
\n" ); document.write( "\n" ); document.write( "6*(3^x)+4*(3^-x)-14=0\r
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Algebra.Com's Answer #172406 by Edwin McCravy(20065)\"\" \"About 
You can put this solution on YOUR website!
I am really struggling to find the answer to this logarithmic equation that we have been set:
\n" ); document.write( "\"+6%2A%283%5Ex%29%2B4%2A%283%5E%28-x%29%29-14=0\"
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document.write( "Divide through by 2 since all coefficients are even:\r\n" );
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document.write( "\"+6%2A%283%5Ex%29%2F2%2B4%2A%283%5E%28-x%29%29%2F2-14%2F2=0%2F2\"\r\n" );
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document.write( "\"3%2A%283%5Ex%29%2B2%2A%283%5E%28-x%29%29-7=0\"\r\n" );
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document.write( "Write \"3%5E%28-x%29\" as \"1%2F%283%5Ex%29\"\r\n" );
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document.write( "\"3%2A%283%5Ex%29%2B2%2A%281%2F3%5Ex%29-7=0\"\r\n" );
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document.write( "Multiply through by \"3%5Ex\" to clear of fractions:\r\n" );
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document.write( "\"3%2A%283%5Ex%29%283%5Ex%29%2B2%2A%281%2F3%5Ex%29%283%5Ex%29-7%283%5Ex%29=0%283%5Ex%29\"\r\n" );
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document.write( "Simplify:\r\n" );
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document.write( "\"3%2A%283%5Ex%29%5E2%2B2%2A%281%2Fcross%283%5Ex%29%29%28cross%283%5Ex%29%29-7%283%5Ex%29=0\"\r\n" );
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document.write( "\"3%2A%283%5Ex%29%5E2%2B2-7%283%5Ex%29=0\"\r\n" );
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document.write( "Replace \"3%5Ex\" by \"u\"\r\n" );
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document.write( "\"3u%5E2%2B2-7u=0\"\r\n" );
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document.write( "Swap the second and third term on the left to get\r\n" );
document.write( "in descending order or powers of \"u\"\r\n" );
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document.write( "\"3u%5E2-7u%2B2=0\"\r\n" );
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document.write( "Factor the left side:\r\n" );
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document.write( "\"%28u-2%29%283u-1%29=0\"\r\n" );
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document.write( "Set each factor = 0\r\n" );
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document.write( "\"u-2=0\"\r\n" );
document.write( "\"u=2\"\r\n" );
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document.write( "\"3u-1=0\"\r\n" );
document.write( "\"3u=1\"\r\n" );
document.write( "\"u=1%2F3\"\r\n" );
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document.write( "For each solution for u, replace \"u\" by \"3%5Ex\"\r\n" );
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document.write( "For \"u=2\", \r\n" );
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document.write( "\"3%5Ex=2\"\r\n" );
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document.write( "Take logs of both side:\r\n" );
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document.write( "\"log%283%5Ex%29=log%282%29\"\r\n" );
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document.write( "Use the principle of logs on the left that]\r\n" );
document.write( "allows you to move an exponent in front of\r\n" );
document.write( "the log:\r\n" );
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document.write( "\"xlog%283%29=log%282%29\"\r\n" );
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document.write( "Divide both sides by \"log%282%29\"\r\n" );
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document.write( "\"x=log%282%29%2F%28log%283%29%29\"\r\n" );
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document.write( "Use your calculator:\r\n" );
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document.write( "\"x=0.6309297536\"\r\n" );
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document.write( "For \"u=1%2F3\", \r\n" );
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document.write( "\"3%5Ex=1%2F3\"\r\n" );
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document.write( "Multiply through by 3 to clear of fractions:\r\n" );
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document.write( "\"3%2A3%5Ex=1\"\r\n" );
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document.write( "Write \"3\" as \"3%5E1\"\r\n" );
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document.write( "\"3%5E1%2A3%5Ex=1\"\r\n" );
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document.write( "Add exponents on the left:\r\n" );
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document.write( "\"3%5E%281%2Bx%29=1\"\r\n" );
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document.write( "Write the \"1\" on the right as \"3%5E0\"\r\n" );
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document.write( "\"3%5E%281%2Bx%29=3%5E0\"\r\n" );
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document.write( "Since the bases are both the same, and positive\r\n" );
document.write( "and not equal to 1, we may equate the\r\n" );
document.write( "exponents:\r\n" );
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document.write( "\"1%2Bx=0\"\r\n" );
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document.write( "\"x=-1\"\r\n" );
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document.write( "So there are two solutions,\r\n" );
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document.write( "\"x=0.6309297536\" and \"x=-1\"\r\n" );
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document.write( "Edwin
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