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Value of $\log_{5} (\frac{1}{25}) = ?$

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- 1

- 4

- 3

- 2

answer is D.

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Detailed Solution

First rewrite as an equation

\log_{5} (\frac{1}{25}) = x

Utilizing the definition of a logarithm, rewrite

\log_{5} (\frac{1}{25}) = x

in exponential form. if

b

is not equal to

1

and both

x

and

b

are positive real numbers.
Here the

\log_{(x)} = y

is equivalent to

b^{y} = x

5^{x} = \frac{1}{25}

In the equation, construct equivalent expressions with the same bases.

5^{x} = 5^{- 2}

The two expressions can only be equivalent since their bases are the same if their exponents are also the same.

x = - 2

x

equals

2

is the variable.

\log_{5} (\frac{1}{25}) = - 2

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