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Answer :
Certainly! Let's solve the equation [tex]\(5^x = \frac{1}{25}\)[/tex] step by step.
1. Recognize the Structure of the Equation: We start with the equation [tex]\(5^x = \frac{1}{25}\)[/tex].
2. Rewrite the Fraction: Notice that [tex]\(\frac{1}{25}\)[/tex] can be expressed using powers of 5 because 25 is a power of 5. Since [tex]\(25 = 5^2\)[/tex], we can write [tex]\(\frac{1}{25}\)[/tex] as:
[tex]\[
\frac{1}{25} = \frac{1}{5^2} = 5^{-2}
\][/tex]
3. Equate the Exponents: Now, our equation becomes [tex]\(5^x = 5^{-2}\)[/tex]. Since the bases are the same, we can set the exponents equal to each other:
[tex]\[
x = -2
\][/tex]
So, the solution to the equation [tex]\(5^x = \frac{1}{25}\)[/tex] is [tex]\(x = -2\)[/tex].
1. Recognize the Structure of the Equation: We start with the equation [tex]\(5^x = \frac{1}{25}\)[/tex].
2. Rewrite the Fraction: Notice that [tex]\(\frac{1}{25}\)[/tex] can be expressed using powers of 5 because 25 is a power of 5. Since [tex]\(25 = 5^2\)[/tex], we can write [tex]\(\frac{1}{25}\)[/tex] as:
[tex]\[
\frac{1}{25} = \frac{1}{5^2} = 5^{-2}
\][/tex]
3. Equate the Exponents: Now, our equation becomes [tex]\(5^x = 5^{-2}\)[/tex]. Since the bases are the same, we can set the exponents equal to each other:
[tex]\[
x = -2
\][/tex]
So, the solution to the equation [tex]\(5^x = \frac{1}{25}\)[/tex] is [tex]\(x = -2\)[/tex].
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