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Evaluate. log_(7)((1)/(4))

Evaluate.\newlinelog⁡714 \log _{7} \frac{1}{4}

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Quotient property of logarithmsright chevron icon

Full solution

Q. Evaluate.\newlinelog⁡714 \log _{7} \frac{1}{4}
  1. Apply Logarithm Property: Use the property of logarithms that allows us to write the log of a quotient as the difference of logs.\newlinelog⁡7(14)=log⁡7(1)−log⁡7(4)\log_{7}\left(\frac{1}{4}\right) = \log_{7}(1) - \log_{7}(4)
  2. Simplify Log of 11: Simplify log⁡7(1)\log_{7}(1) since the log of 11 to any base is 00.\newlinelog⁡7(1)=0\log_{7}(1) = 0
  3. Subtract Logs: Now we have 0−log⁡7(4)0 - \log_{7}(4). So, log⁡7(14)=0−log⁡7(4)\log_{7}\left(\frac{1}{4}\right) = 0 - \log_{7}(4)
  4. Final Simplification: Simplify the expression. log⁡7(14)=−log⁡7(4)\log_{7}\left(\frac{1}{4}\right) = -\log_{7}(4)

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