This problem requires logs I think. It isn't as straightforward as most exponent problems on the gmat. This is how I solved it:
10/(1+10^-x)=2
2(1+10^-x)=10
1+10^(-x)=5
10^(-x)=4
take the log base 10 of both sides and you get -x=ln 4/1n 10 <-- Change of base rule.
x=-ln 4/ ln 10= approx. -.6021.
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