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

log⁡155= \log _{\frac{1}{5}} 5=

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Add and subtract rational numbersright chevron icon

Full solution

Q. log⁡155= \log _{\frac{1}{5}} 5=
  1. Identify Base and Argument: Identify the base of the logarithm and the argument. The base is (15)(\frac{1}{5}) and the argument is 55.
  2. Recall Logarithm Definition: Recall the definition of a logarithm: log⁡base(argument)=exponent\log_{\text{base}}(\text{argument}) = \text{exponent} means that baseexponent=argument\text{base}^{\text{exponent}} = \text{argument}.
  3. Determine Exponent: Determine the exponent that makes (15)(\frac{1}{5}) raised to that power equal to 55. Since (15)−1=5(\frac{1}{5})^{-1} = 5, the exponent we are looking for is −1-1.
  4. Conclude Solution: Conclude that log⁡(15)5=−1\log_{\left(\frac{1}{5}\right)}5 = -1 because (15)−1=5\left(\frac{1}{5}\right)^{-1} = 5.

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