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ozzi
3 years ago
7

Simplify: log base 3 (1/3) ...?

Mathematics
1 answer:
yarga [219]3 years ago
6 0
The answer is 1.

log_3( \frac{1}{3} )
_____
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)}
_____
Since \frac{1}{x} = x^{-1}, then: \frac{log_{10} ( \frac{1}{3}) }{log_{10}(3)} = \frac{log_{10}(3^{-1} )}{log_{10}(3)}
_____
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

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