document.write( "Question 21503: 2^(1-x)=3^x x=?
\n" ); document.write( "please tell me how to solve this question \n" ); document.write( "

Algebra.Com's Answer #10401 by Earlsdon(6294) $\"\"$ $\"About$

You can put this solution on YOUR website!
Using logarithms:\r
\n" ); document.write( "\n" ); document.write( " $\"2%5E%281-x%29+=+3%5Ex\"$ Take the log of both sides.
\n" ); document.write( " $\"%281-x%29log2+=+xlog3\"$ Expand the left side using the distributive property.
\n" ); document.write( " $\"log2+-+xlog2+=+xlog3\"$ Add xlog2 to both sides.
\n" ); document.write( " $\"log2+=+xlog3+%2B+xlog2\"$ Factor the x.
\n" ); document.write( " $\"log2+=+x%28log3+%2B+log2%29\"$ Simplify the right side.(loga+logb=log(ab))
\n" ); document.write( " $\"log2+=+xlog6\"$ Divide both sides by log6
\n" ); document.write( " $\"x+=+%28log2%29%2Flog6\"$ Evaluate using your calculator or table of logarithms.
\n" ); document.write( " $\"x+=+0.3868528\"$ \r
\n" ); document.write( "\n" ); document.write( "Check:
\n" ); document.write( " $\"2%5E%281-0.3868528%29+=+2%5E0.6131472\"$ = 1.5295923...
\n" ); document.write( " $\"3%5E0.3868528+=+1.5295923\"$ \n" ); document.write( "

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