document.write( "Question 241462: 6e^(2x)-16e^x=6\r
\n" ); document.write( "\n" ); document.write( "solve for x. please explain \n" ); document.write( "
Algebra.Com's Answer #176856 by stanbon(75887)\"\" \"About 
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6e^(2x)-16e^x=6
\n" ); document.write( "solve for x. please explain
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\n" ); document.write( "This is a quadratic equation with e^x as it's variable:
\n" ); document.write( "Rewrite:
\n" ); document.write( "6(e^x)^2 - 16(e^x) - 6 = 0
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\n" ); document.write( "Let m = e^x
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\n" ); document.write( "6m^2 - 16m - 6 = 0
\n" ); document.write( "3m^2 - 8m - 3 = 0
\n" ); document.write( "---
\n" ); document.write( "3m^2 -9m+m - 3 = 0
\n" ); document.write( "3m(m-3)+(m-3) = 0
\n" ); document.write( "(m-3)(3m+1) = 0
\n" ); document.write( "m = 3 or m = -1/3
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\n" ); document.write( "Substitute to solve for \"x\":
\n" ); document.write( "e^x = 3
\n" ); document.write( "x = ln(3) = 1.098612...
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\n" ); document.write( "e^x = (-1/3)
\n" ); document.write( "No solution because no value of e is negative.
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\n" ); document.write( "Cheers,
\n" ); document.write( "Stan H.
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