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

What is the value of $\log _{6} 216 ?$ $\newline$ Answer:

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Product property of logarithms

Full solution

Q. What is the value of

\log _{6} 216 ?

\newline

Answer:

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 $3$ .

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