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Answer :
To solve the equation
[tex]$$
5^x = \frac{1}{25},
$$[/tex]
follow these steps:
1. Notice that [tex]$25$[/tex] can be written as [tex]$5^2$[/tex]. Therefore, we have:
[tex]$$
\frac{1}{25} = \frac{1}{5^2} = 5^{-2}.
$$[/tex]
2. Now, the equation becomes:
[tex]$$
5^x = 5^{-2}.
$$[/tex]
3. Since the bases are the same, the exponents must be equal. Thus, we set:
[tex]$$
x = -2.
$$[/tex]
The solution to the equation is
[tex]$$
x = -2.
$$[/tex]
[tex]$$
5^x = \frac{1}{25},
$$[/tex]
follow these steps:
1. Notice that [tex]$25$[/tex] can be written as [tex]$5^2$[/tex]. Therefore, we have:
[tex]$$
\frac{1}{25} = \frac{1}{5^2} = 5^{-2}.
$$[/tex]
2. Now, the equation becomes:
[tex]$$
5^x = 5^{-2}.
$$[/tex]
3. Since the bases are the same, the exponents must be equal. Thus, we set:
[tex]$$
x = -2.
$$[/tex]
The solution to the equation is
[tex]$$
x = -2.
$$[/tex]
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