What is the value of log_(6)216? Answer:

Recognize Relationship: Recognize the relationship between the base of the logarithm and the number. We need to find log base 6 of 216. We should check if 216 is a power of 6, as this will simplify the calculation.Express as Power: Express 216 as a power of 6. 216 can be written as 6^3 because 6 * 6 * 6 = 216.Apply Logarithm Definition: Apply the definition of a logarithm. Using the fact that log base b of b^x equals x, we can write log base 6 of 6^3 as 3. log_(6)216 = log_(6)(6^3) = 3Verify Result: Verify the result. Since 6^3 indeed equals 216, the logarithm log base 6 of 216 is correctly evaluated as 3.

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What is the value of
log_(6)216?
Answer:

Evaluate. $\newline$ $\log _{6} 216$ $\newline$ Write your answer in simplest form.

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Precalculus

Product property of logarithms

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Q. Evaluate.

\newline

\log _{6} 216

\newline

Write your answer in simplest form.

Recognize Relationship: Recognize the relationship between the base of the logarithm and the number. $\newline$ We need to find $\log_{6} 216$ . We should check if $216$ is a power of $6$ , as this will simplify the calculation.
Express as Power: Express $216$ as a power of $6$ . $\newline$ $216$ can be written as $6^3$ because $6 \times 6 \times 6 = 216$ .
Apply Logarithm Definition: Apply the definition of a logarithm. $\newline$ Using the fact that $\log_{b} b^{x} = x$ , we can write $\log_{6} 6^{3}$ as $3$ . $\newline$ $\log_{6}216 = \log_{6}(6^{3}) = 3$
Verify Result: Verify the result. $\newline$ Since $6^3$ indeed equals $216$ , the logarithm $\log_{6} 216$ is correctly evaluated as $3$ .