document.write( "Question 71077: I have a work sheet w/ some natural logs that I need help with.\r
\n" ); document.write( "\n" ); document.write( "e^x * e^(3x) = 4\r
\n" ); document.write( "\n" ); document.write( "e^9 = (e^x)^3 (1/e^9)\r
\n" ); document.write( "\n" ); document.write( "Thank you so much! \n" ); document.write( "

Algebra.Com's Answer #50805 by jim_thompson5910(35256) $\"\"$ $\"About$

You can put this solution on YOUR website!
$\"e%5Ex+%2A+e%5E%283x%29+=+4\"$ Start with given expression
\n" ); document.write( " $\"e%5E%28x%2B3x%29+=+4\"$ The left side can be written as $\"e%5E%28x%2B3x%29\"$ since $\"e%5Ex%2Ae%5Ey=e%5E%28x%2By%29\"$
\n" ); document.write( " $\"ln%28e%5E%28x%2B3x%29%29+=ln+4\"$ Take natural log of both sides, this undoes the natural base e
\n" ); document.write( " $\"4x=ln+4\"$ Solve for x by dividing both sides by 4
\n" ); document.write( " $\"x=%28ln+4%29%2F4=0.34657359\"$ Approximately
\n" ); document.write( "

\n" ); document.write( "Do the same thing to the next problem
\n" ); document.write( " $\"e%5E9+=+%28e%5Ex%29%5E3+%281%2Fe%5E9%29\"$ Start with given expression
\n" ); document.write( " $\"e%5E9+=+e%5E%283%2Ax%29%2Fe%5E9\"$ The right side can be rewritten as $\"e%5E%283x%29\"$ since $\"e%5Ex%5Ey=e%5E%28x%2Ay%29\"$ (in other words $\"e%5Ex%5E3=e%5E%283x%29\"$ )
\n" ); document.write( " $\"e%5E18+=+e%5E%283%2Ax%29\"$ Multiply both side by e^9
\n" ); document.write( " $\"ln%28e%5E18%29+=ln+%28e%5E%283%2Ax%29%29\"$ Take natural log of both sides, this undoes the natural base e
\n" ); document.write( " $\"18+=+3%2Ax\"$ Solve for x by dividing both sides by 3
\n" ); document.write( " $\"x=18%2F3=6\"$ \n" ); document.write( "

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