Identify base and argument: Identify the base and the argument of the logarithm. The base of the logarithm is (1)/(3) and the argument is 81.Express as power of base: Express 81 as a power of (1)/(3). We know that 81 is 3^4, so we can write 81 as ((1)/(3))^(-4).Rewrite logarithm with power of base: Rewrite the logarithm using the argument expressed as a power of the base. log_((1)/(3))81 becomes log_((1)/(3))((1)/(3))^(-4).Apply property of logarithms: Apply the property of logarithms that 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.

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$\log _{\frac{1}{3}} 81=$

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Algebra 2

Evaluate logarithms using properties

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\log _{\frac{1}{3}} 81=

Identify base and argument: Identify the base and the argument of the logarithm. $\newline$ The base of the logarithm is $\frac{1}{3}$ and the argument is $81$ .
Express as power of base: Express $81$ as a power of $(1)/(3)$ . $\newline$ We know that $81$ is $3^4$ , so we can write $81$ as $((1)/(3))^{-4}$ .
Rewrite logarithm with power of base: Rewrite the logarithm using the argument expressed as a power of the base. $\newline$ $\log_{\frac{1}{3}} 81$ becomes $\log_{\frac{1}{3}}\left(\frac{1}{3}\right)^{-4}$ .
Apply property of logarithms: Apply the property of logarithms that $\log_b(b^x) = x$ . Since the base of the logarithm and the base of the exponent are the same, we can simplify the expression to $-4$ .