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Basic Logarithm question

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If I have -log(0.1/x) = .16 , how do I get rid of the log to solve for x?

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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

            
        

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