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Answer :
We are given the logarithmic equation
[tex]$$
\log_{5} \frac{1}{25} = -2.
$$[/tex]
Recall the definition of a logarithm: For any positive numbers [tex]$a$[/tex], [tex]$b$[/tex] (with [tex]$b \neq 1$[/tex]), and [tex]$c$[/tex], the equation
[tex]$$
\log_b a = c
$$[/tex]
is equivalent to the exponential equation
[tex]$$
b^c = a.
$$[/tex]
Here, we have:
- Base: [tex]$b = 5$[/tex],
- Exponent: [tex]$c = -2$[/tex],
- Result: [tex]$a = \frac{1}{25}$[/tex].
Thus, using the definition, the logarithmic equation can be written in exponential form as
[tex]$$
5^{-2} = \frac{1}{25}.
$$[/tex]
This is the desired conversion of the given logarithmic equation into its exponential form.
[tex]$$
\log_{5} \frac{1}{25} = -2.
$$[/tex]
Recall the definition of a logarithm: For any positive numbers [tex]$a$[/tex], [tex]$b$[/tex] (with [tex]$b \neq 1$[/tex]), and [tex]$c$[/tex], the equation
[tex]$$
\log_b a = c
$$[/tex]
is equivalent to the exponential equation
[tex]$$
b^c = a.
$$[/tex]
Here, we have:
- Base: [tex]$b = 5$[/tex],
- Exponent: [tex]$c = -2$[/tex],
- Result: [tex]$a = \frac{1}{25}$[/tex].
Thus, using the definition, the logarithmic equation can be written in exponential form as
[tex]$$
5^{-2} = \frac{1}{25}.
$$[/tex]
This is the desired conversion of the given logarithmic equation into its exponential form.
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