Identify Base and Argument: Identify the base and the argument of the logarithm. The base of the logarithm is 6, and the argument is 36.Express as Power of 6: Express 36 as a power of 6. 36 is 6 squared, which means 36 = 6^2.Rewrite Using Power: Rewrite the logarithm using the argument expressed as a power of the base. log_(6)36 becomes log_(6)(6^2).Apply Power Property: Apply the power property of logarithms. The power property states that log_b(a^c) = c * log_b(a). Therefore, log_(6)(6^2) is 2 * log_(6)6.Evaluate Logarithm: Evaluate log_(6)6. The logarithm of a number to the same base is always 1. Therefore, log_(6)6 is 1.Multiply Result: Multiply the result from Step 5 by the exponent from Step 4. 2 * log_(6)6 is 2 * 1, which equals 2.

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$\log _{6} 36=$

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Algebra 2

Evaluate logarithms using properties

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\log _{6} 36=

Identify Base and Argument: Identify the base and the argument of the logarithm. $\newline$ The base of the logarithm is $6$ , and the argument is $36$ .
Express as Power of $6$ : Express $36$ as a power of $6$ . $\newline$ $36$ is $6$ squared, which means $36 = 6^2$ .
Rewrite Using Power: Rewrite the logarithm using the argument expressed as a power of the base. $\log_{6}36$ becomes $\log_{6}(6^2)$ .
Apply Power Property: Apply the power property of logarithms. The power property states that $\log_b(a^c) = c \cdot \log_b(a)$ . Therefore, $\log_{6}(6^2)$ is $2 \cdot \log_{6}6$ .
Evaluate Logarithm: Evaluate $\log_{6}6$ . The logarithm of a number to the same base is always $1$ . Therefore, $\log_{6}6$ is $1$ .
Multiply Result: Multiply the result from Step $5$ by the exponent from Step $4$ . $\newline$ $2 \times \log_{6}6$ is $2 \times 1$ , which equals $2$ .