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Answer :
To rewrite the logarithmic equation
[tex]$$
\log_5 \frac{1}{25} = -2
$$[/tex]
in exponential form, we start by recalling the definition of a logarithm:
[tex]$$
\log_b(a) = c \quad \Longleftrightarrow \quad b^c = a.
$$[/tex]
Here, we have:
- The base [tex]$b = 5$[/tex],
- The result [tex]$a = \frac{1}{25}$[/tex], and
- The exponent [tex]$c = -2$[/tex].
Using the definition, we convert the logarithmic equation to its exponential form:
[tex]$$
5^{-2} = \frac{1}{25}.
$$[/tex]
Thus, the equivalent exponential form of the given logarithmic equation is
[tex]$$
5^{-2} = \frac{1}{25}.
$$[/tex]
[tex]$$
\log_5 \frac{1}{25} = -2
$$[/tex]
in exponential form, we start by recalling the definition of a logarithm:
[tex]$$
\log_b(a) = c \quad \Longleftrightarrow \quad b^c = a.
$$[/tex]
Here, we have:
- The base [tex]$b = 5$[/tex],
- The result [tex]$a = \frac{1}{25}$[/tex], and
- The exponent [tex]$c = -2$[/tex].
Using the definition, we convert the logarithmic equation to its exponential form:
[tex]$$
5^{-2} = \frac{1}{25}.
$$[/tex]
Thus, the equivalent exponential form of the given logarithmic equation is
[tex]$$
5^{-2} = \frac{1}{25}.
$$[/tex]
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