First get rid of the minus sign by negating both sides.
log(0.1/x) = -0.16.
The opposite of log is raising to a power. If these are base 10 logs, raise 10 to the power of both sides.
0.1/x = 10^(-0.16) = 0.692.
Now you can rearrange to solve for x.
0.1 = 0.692x
x = 0.1/0.692 = 0.145
Note: Another thing you could have done with the minus sign is bring it inside the log, as n * log(a) = log(a^n). So -1 * log(a) = log(a^-1) = log(1/a). That is, the log of a reciprocal is the negative of the log.
In other words -log(0.1/x) = log(x/0.1).
Now raise 10 to the power of both sides.
log(x/0.1) = 0.16
x/0.1 = 10^0.16 = 1.45
x = 1.45*0.1 = 0.145