Identify the relationship: Identify the relationship between the base of the logarithm and the number. The base of the logarithm is 3, and we need to find the exponent that 3 must be raised to in order to get 81.Express 81 as a power: Express 81 as a power of 3. 81 is 3 raised to the power of 4, since 3 * 3 * 3 * 3 = 81.Apply the definition of a logarithm: Apply the definition of a logarithm. Since 81 is 3^4, we can write log_(3)81 as log_(3)(3^4).Use the property of logarithms: Use the property of logarithms that log_b(b^x) = x. According to this property, log_(3)(3^4) simplifies to 4.

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$\log _{3} 81=$

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Algebra 2

Evaluate logarithms using properties

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\log _{3} 81=

Identify the relationship: Identify the relationship between the base of the logarithm and the number. $\newline$ The base of the logarithm is $3$ , and we need to find the exponent that $3$ must be raised to in order to get $81$ .
Express $81$ as a power: Express $81$ as a power of $3$ . $\newline$ $81$ is $3$ raised to the power of $4$ , since $3 \times 3 \times 3 \times 3 = 81$ .
Apply the definition of a logarithm: Apply the definition of a logarithm. $\newline$ Since $81$ is $3^4$ , we can write $\log_{3}81$ as $\log_{3}(3^4)$ .
Use the property of logarithms: Use the property of logarithms that $\log_b(b^x) = x$ . According to this property, $\log_{3}(3^4)$ simplifies to $4$ .