SOLUTION: 2^(1-x)=3^x x=? please tell me how to solve this question

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Question 21503: 2^(1-x)=3^x x=?
please tell me how to solve this question
Answer by Earlsdon(6294) About Me  (Show Source):
You can put this solution on YOUR website!
Using logarithms:
2%5E%281-x%29+=+3%5Ex Take the log of both sides.
%281-x%29log2+=+xlog3 Expand the left side using the distributive property.
log2+-+xlog2+=+xlog3 Add xlog2 to both sides.
log2+=+xlog3+%2B+xlog2 Factor the x.
log2+=+x%28log3+%2B+log2%29 Simplify the right side.(loga+logb=log(ab))
log2+=+xlog6 Divide both sides by log6
x+=+%28log2%29%2Flog6 Evaluate using your calculator or table of logarithms.
x+=+0.3868528
Check:
2%5E%281-0.3868528%29+=+2%5E0.6131472 = 1.5295923...
3%5E0.3868528+=+1.5295923