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
