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25. [tex]\(\log_{a} 1 =\)[/tex]

A. 0

B. 1

C. [tex]\(a\)[/tex]

D. 10

Sagot :

GinnyAnsweridn
To solve the logarithmic expression [tex]\( \log_a 1 \)[/tex], we need to understand the fundamental properties of logarithms.

The logarithm [tex]\( \log_a b \)[/tex] answers the question: "To what exponent must we raise [tex]\( a \)[/tex], to obtain [tex]\( b \)[/tex]?"

Let's denote [tex]\( \log_a 1 \)[/tex] by [tex]\( x \)[/tex]. Therefore, we have the following equation to solve for [tex]\( x \)[/tex]:

[tex]\[ a^x = 1 \][/tex]

We need to determine the value of [tex]\( x \)[/tex] such that [tex]\( a \)[/tex] raised to the power [tex]\( x \)[/tex] equals 1. It is a well-known fact that any number raised to the power 0 is equal to 1. Mathematically, this is expressed as:

[tex]\[ a^0 = 1 \][/tex]

From this property, it follows that:

[tex]\[ x = 0 \][/tex]

Therefore, the value of [tex]\( \log_a 1 \)[/tex] is 0.

So, the correct answer is:
(a) 0
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