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log_(3)27=

$\log _{3} 27=$

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Relationship between squares and square roots

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Q.

\log _{3} 27=

Problem Statement: We are asked to find the value of $\log_{3}27$ . The logarithm $\log_{b}a$ answers the question: ＂To what power must the base $b$ be raised, to produce the number $a$ ?＂ In this case, we want to know to what power we must raise $3$ to get $27$ .
Identifying the Power of $3$ : We know that $27$ is a power of $3$ because $3^3 = 27$ . This means that the exponent to which the base $3$ must be raised to get $27$ is $3$ .
Calculating the Logarithm: Therefore, $\log_{3}27$ is equal to $3$ , because $3$ raised to the power of $3$ gives us $27$ .

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