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log_((1)/(3))81=

log⁡1381= \log _{\frac{1}{3}} 81=

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Full solution

Q. log⁡1381= \log _{\frac{1}{3}} 81=
  1. Identify base and argument: Identify the base and the argument of the logarithm.\newlineThe base of the logarithm is 13\frac{1}{3} and the argument is 8181.
  2. Express as power of base: Express 8181 as a power of (1)/(3)(1)/(3).\newlineWe know that 8181 is 343^4, so we can write 8181 as ((1)/(3))−4((1)/(3))^{-4}.
  3. Rewrite logarithm with power of base: Rewrite the logarithm using the argument expressed as a power of the base. \newlinelog⁡1381\log_{\frac{1}{3}} 81 becomes log⁡13(13)−4\log_{\frac{1}{3}}\left(\frac{1}{3}\right)^{-4}.
  4. Apply property of logarithms: Apply the property of logarithms that log⁡b(bx)=x\log_b(b^x) = x. Since the base of the logarithm and the base of the exponent are the same, we can simplify the expression to −4-4.

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