The answer is 1.
\(log_3( \frac{1}{3} )\)
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Since \(log_y(x) = \frac{log_{10}(x)}{log_{10}(y)}\), then: \(log_3( \frac{1}{3} )= \frac{log_{10} ( \frac{1}{3}) }{log_{10}(3)}\)
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Since \(\frac{1}{x} = x^{-1}\), then: \(\frac{log_{10} ( \frac{1}{3}) }{log_{10}(3)} = \frac{log_{10}(3^{-1} )}{log_{10}(3)}\)
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Since \(log x^{a} =a*logx\), then: \(\frac{log_{10}(3^{-1} )}{log_{10}(3)}= \frac{-1*log_{10}(3)}{log_{10}(3)}\)
From here: \(\frac{-1*log_{10}(3)}{log_{10}(3)}=-1*\frac{log_{10}(3)}{log_{10}(3)}=-1*1 = -1\)
