Math  /  Algebra

QuestionDetermine if the statement is true or false. If the statement is true, write a proof. If the statement is false, provide a counterexample. Assume that the variable represents a positive real number. log5(1r)=1log5r\log _{5}\left(\frac{1}{r}\right)=\frac{1}{\log _{5} r}

Studdy Solution
Provide a counterexample to illustrate the difference.
Consider r=5r = 5: log5(15)=log5(51)=1 \log_{5}\left(\frac{1}{5}\right) = \log_{5}(5^{-1}) = -1 1log5(5)=11=1 \frac{1}{\log_{5}(5)} = \frac{1}{1} = 1 The expressions 1-1 and 11 are not equal, confirming the statement is false.
Solution: The statement is false.

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