document.write( "Question 126824: How do you solve the exponential equation -5e^-x+9=6 \n" ); document.write( "
Algebra.Com's Answer #92897 by Earlsdon(6294)\"\" \"About 
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Solve for x:
\n" ); document.write( "\"-5%2Ae%5E%28-x%29+%2B+9+=+6\" Subtract 9 from both sides.
\n" ); document.write( "\"-5%2Ae%5E%28-x%29+=+-3\" Divide both sides by -5.
\n" ); document.write( "\"e%5E%28-x%29+=+3%2F5\"
\n" ); document.write( "\"1%2Fe%5Ex+=+3%2F5\" Invert both sides.
\n" ); document.write( "\"e%5Ex+=+5%2F3\" Now take the natural log of both sides.
\n" ); document.write( "\"ln%28e%29%5Ex+=+ln%285%2F3%29\"
\n" ); document.write( "\"x%2Aln%28e%29+=+ln%285%2F3%29\" But \"ln%28e%29+=+1\", so...
\n" ); document.write( "\"x+=+0.512\"
\n" ); document.write( "Check:
\n" ); document.write( "\"-5%2Ae%5E%28-x%29+%2B+9+=+6\" Substitute x = 0.512
\n" ); document.write( "\"-5%2Ae%5E%28-0.512%29+%2B+9+=+6\"
\n" ); document.write( "\"-5%2A0.6%2B9+=+6\"
\n" ); document.write( "\"-3%2B9+=+6\"
\n" ); document.write( "\"6+=+6\"
\n" ); document.write( "
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