document.write( "Question 752558: Use common or natural logarithms to solve the exponential equation symbolically. 2e^(6x+3)=4 \n" ); document.write( "

Algebra.Com's Answer #457842 by Earlsdon(6294) $\"\"$ $\"About$

You can put this solution on YOUR website!
Use natural logs to solve:
\n" ); document.write( " $\"2e%5E%286x%2B3%29+=+4\"$ Divide both sides by 2.
\n" ); document.write( " $\"e%5E%286x%2B3%29+=+2\"$ Take the natural log of both sides.
\n" ); document.write( " $\"ln%28e%5E%286x%2B3%29%29+=+ln%282%29\"$ Apply the power rule for logarithms to the left side.
\n" ); document.write( " $\"%286x%2B3%29ln%28e%29+=+ln%282%29\"$ Substitute $\"ln%28e%29+=+1\"$
\n" ); document.write( " $\"6x%2B3+=+ln%282%29\"$ Subtract 3 from both sides.
\n" ); document.write( " $\"6x+=+ln%282%29-3\"$ Divide both sides by 6.
\n" ); document.write( " $\"x+=+%28ln%282%29-3%29%2F6%29\"$ Evaluate.
\n" ); document.write( " $\"x+=+-0.3844\"$
\n" ); document.write( " \n" ); document.write( "

\n" );