Evaluate: log_(125)5 Answer:

Recognize Relationship: Recognize the relationship between the base of the logarithm and the number. We have log base 125 of 5, which can be written as log_(125)(5). We need to find the power to which 125 must be raised to get 5. Since 125 is 5^3, we are looking for an exponent that relates 5^3 to 5.Express as Power: Express 5 as a power of 125. We know that 125 = 5^3, so we can write 5 as 5^(3/3) which simplifies to 5^(1/3). Therefore, 5 is 125 raised to the power of 1/3.Apply Logarithm Definition: Apply the definition of a logarithm. By the definition of a logarithm, if 125^(1/3) = 5, then log_(125)(5) = 1/3.

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Evaluate: $\newline$ $\log _{125} 5$ $\newline$ Answer:

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Precalculus

Product property of logarithms

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Q. Evaluate:

\newline

\log _{125} 5

\newline

Answer:

Recognize Relationship: Recognize the relationship between the base of the logarithm and the number. $\newline$ We have $\log_{125}(5)$ , which can be written as $\log_{125}(5)$ . We need to find the power to which $125$ must be raised to get $5$ . Since $125$ is $5^3$ , we are looking for an exponent that relates $5^3$ to $5$ .
Express as Power: Express $5$ as a power of $125$ . We know that $125 = 5^3$ , so we can write $5$ as $5^{(3/3)}$ which simplifies to $5^{(1/3)}$ . Therefore, $5$ is $125$ raised to the power of $1/3$ .
Apply Logarithm Definition: Apply the definition of a logarithm. $\newline$ By the definition of a logarithm, if $125^{1/3} = 5$ , then $\log_{125}(5) = 1/3$ .