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log_((1)/(5))5=

$\log _{\frac{1}{5}} 5=$

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Add and subtract rational numbers

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Q.

\log _{\frac{1}{5}} 5=

Identify Base and Argument: Identify the base of the logarithm and the argument. The base is $(\frac{1}{5})$ and the argument is $5$ .
Recall Logarithm Definition: Recall the definition of a logarithm: $\log_{\text{base}}(\text{argument}) = \text{exponent}$ means that $\text{base}^{\text{exponent}} = \text{argument}$ .
Determine Exponent: Determine the exponent that makes $(\frac{1}{5})$ raised to that power equal to $5$ . Since $(\frac{1}{5})^{-1} = 5$ , the exponent we are looking for is $-1$ .
Conclude Solution: Conclude that $\log_{\left(\frac{1}{5}\right)}5 = -1$ because $\left(\frac{1}{5}\right)^{-1} = 5$ .

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