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Answer :
We start by rewriting the argument of the logarithm:
[tex]$$
\frac{1}{25} = \frac{1}{5^2} = 5^{-2}.
$$[/tex]
Now, by the definition of logarithms, the expression
[tex]$$
\log_5 \left( 5^{-2} \right)
$$[/tex]
represents the exponent we need to raise 5 to in order to obtain [tex]$5^{-2}$[/tex]. Since [tex]$5^{-2}$[/tex] is already in exponential form, it follows directly that
[tex]$$
\log_5 \left( 5^{-2} \right) = -2.
$$[/tex]
Thus, the value of the logarithm is
[tex]$$
\boxed{-2}.
$$[/tex]
[tex]$$
\frac{1}{25} = \frac{1}{5^2} = 5^{-2}.
$$[/tex]
Now, by the definition of logarithms, the expression
[tex]$$
\log_5 \left( 5^{-2} \right)
$$[/tex]
represents the exponent we need to raise 5 to in order to obtain [tex]$5^{-2}$[/tex]. Since [tex]$5^{-2}$[/tex] is already in exponential form, it follows directly that
[tex]$$
\log_5 \left( 5^{-2} \right) = -2.
$$[/tex]
Thus, the value of the logarithm is
[tex]$$
\boxed{-2}.
$$[/tex]
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