document.write( "Question 74031: please help me with this equation.thanks so much\r
\n" ); document.write( "\n" ); document.write( "If log 2=.3010 log3=.4771, find the numerical value of x in 3^x+2=405. \n" ); document.write( "

Algebra.Com's Answer #53045 by jim_thompson5910(35256) $\"\"$ $\"About$

You can put this solution on YOUR website!
$\"3%5Ex%2B2=405\"$
\n" ); document.write( " $\"3%5Ex=403\"$ Subtract 2 from both sides
\n" ); document.write( " $\"log_%5B3%5D%283%5Ex%29=log_%5B3%5D%28403%29\"$ Take the log base 3 of both sides
\n" ); document.write( " $\"x=log_%5B3%5D%28403%29\"$
\n" ); document.write( "Use the change of base formula
\n" ); document.write( " $\"log_%5Bb%5D%28a%29=%28log+%28a%29%29%2F%28log%28b%29%29\"$
\n" ); document.write( " $\"x=%28log+%28403%29%29%2F%28log%283%29%29\"$ Remember the default base is 10
\n" ); document.write( " $\"x=2.605305%2F.4771\"$ Use given value log3=.4771 and evaluate log 403
\n" ); document.write( " $\"x=5.46071\"$ Approximately
\n" ); document.write( "Hope this helps.
\n" ); document.write( "

\n" ); document.write( "Check:
\n" ); document.write( " $\"3%5Ex%2B2=405\"$ Plug in x=5.46071
\n" ); document.write( " $\"3%5E%285.46071%29%2B2=405\"$
\n" ); document.write( " $\"403.107%2B2=405\"$
\n" ); document.write( " $\"405.107=405\"$ Which is close but off due to roundoff errors. \n" ); document.write( "

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