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Answer :
Answer:
A
Step-by-step explanation:
using the rule of logarithms
• [tex]log_{b}[/tex] x = n ⇒ x = [tex]b^{n}[/tex]
given
[tex]log_{5}[/tex] ( [tex]\frac{1}{25}[/tex] ) = - 2 , then
[tex]\frac{1}{25}[/tex] = [tex]5^{-2}[/tex] ← option A
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Final answer:
The exponential form of the logarithmic equation log₅(1/25) = -2 is 5⁻² = 1/25.
Explanation:
The given logarithmic equation is log₅(1/25) = -2. To convert this into an exponential form, we have to understand that in a logarithm, the base raised to the result is equal to the argument. Therefore, the base in this case is 5, the result is -2, and the argument is 1/25. Thus, we can write this equation in exponential form as 5⁻² = 1/25. So the correct answer is option A. This is due to the properties of logarithms which state that the logarithm of a number raised to an exponent is the product of the exponent and the logarithm of the number.
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