document.write( "Question 64477: Please help.
\n" ); document.write( "log base3(x-2)+log base3(x+4)=3
\n" ); document.write( "e^x+5=8
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Algebra.Com's Answer #45110 by Earlsdon(6294) $\"\"$ $\"About$

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Solve for x:
\n" ); document.write( " $\"log3%28x-2%29%2Blog3%28x%2B4%29+=+3\"$ Applying the product rule for logarithms: $\"log%28M%29%2Blog%28N%29+=+log%28%28MN%29%29\"$ we get:
\n" ); document.write( " $\"log3%28%28x-2%29%28x%2B4%29%29+=+3\"$ Simplifying:
\n" ); document.write( " $\"log3%28x%5E2%2B2x-8%29+=+3\"$ Writing this in exponential form: $\"logb%28x%29+=+y\"$ means $\"b%5Ey+=+x\"$
\n" ); document.write( " $\"3%5E3+=+x%5E2%2B2x-8\"$ Simplify:
\n" ); document.write( " $\"x%5E2%2B2x-17+=+0\"$ Solving by the quadratic formula: $\"x+=+%28-b%2B-sqrt%28b%5E2-4ac%29%29%2F2a\"$
\n" ); document.write( " $\"x+=+%28-2%2B-sqrt%282%5E2-4%281%29%28-17%29%29%29%2F2%281%29\"$ Simplifying:
\n" ); document.write( " $\"x+=+%28-2%2B-sqrt%2872%29%29%2F2\"$ Simplifying further:
\n" ); document.write( " $\"x+=+%28-2%2B-sqrt%2836%2A2%29%29%2F2\"$
\n" ); document.write( " $\"x+=+-1%2B3sqrt%282%29\"$ and $\"x+=+-1-3sqrt%282%29\"$
\n" ); document.write( "-------------------------------------------------
\n" ); document.write( "Solve for x:
\n" ); document.write( " $\"e%5Ex+%2B+5+=+8\"$ Subtract 5 from both sides.
\n" ); document.write( " $\"e%5Ex+=+3\"$ Take the natural log of both sides.
\n" ); document.write( " $\"xln%28e%29+=+ln%283%29\"$ But $\"ln%28e%29+=+1\"$ , so:
\n" ); document.write( " $\"x+=+ln%283%29\"$
\n" ); document.write( " $\"x+=+1.0986\"$ Approx. \n" ); document.write( "

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