What is the value of log_(5)((1)/(5)) ? Answer:

Identify Base and Argument: Identify the base and the argument of the logarithm. We are given the logarithm log base 5 of (1/5), which means we are looking for the power to which 5 must be raised to get 1/5.Apply Logarithm Definition: Apply the definition of a logarithm. The definition of a logarithm states that if log base b of a equals c, then b^c = a. In this case, we want to find c such that 5^c = 1/5.Recognize Base-Argument Relationship: Recognize the relationship between the base and the argument. Since 1/5 is 5^-1 (because any number to the negative first power is the reciprocal of that number), we can see that 5^c = 5^-1.Equate Exponents: Equate the exponents. If 5^c = 5^-1, then by the property of equality for exponential expressions, c must be equal to -1.Conclude Logarithm Value: Conclude the value of the logarithm. Therefore, log base 5 of 1/5 is equal to -1.

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What is the value of
log_(5)((1)/(5)) ?
Answer:

Evaluate. $\newline$ $\log _{5} \frac{1}{5}$ $\newline$ Write your answer in simplest form.

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Precalculus

Quotient property of logarithms

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Q. Evaluate.

\newline

\log _{5} \frac{1}{5}

\newline

Write your answer in simplest form.

Identify Base and Argument: Identify the base and the argument of the logarithm. $\newline$ We are given the logarithm $\log_{5}(\frac{1}{5})$ , which means we are looking for the power to which $5$ must be raised to get $\frac{1}{5}$ .
Apply Logarithm Definition: Apply the definition of a logarithm. $\newline$ The definition of a logarithm states that if $\log_{b}a = c$ , then $b^{c} = a$ . In this case, we want to find $c$ such that $5^{c} = \frac{1}{5}$ .
Recognize Base-Argument Relationship: Recognize the relationship between the base and the argument. $\newline$ Since $\frac{1}{5}$ is $5^{-1}$ (because any number to the negative first power is the reciprocal of that number), we can see that $5^c = 5^{-1}.$
Equate Exponents: Equate the exponents. $\newline$ If $5^c = 5^{-1}$ , then by the property of equality for exponential expressions, $c$ must be equal to $-1$ .
Conclude Logarithm Value: Conclude the value of the logarithm. $\newline$ Therefore, $\log_{5} \frac{1}{5}$ is equal to $-1$ .