To solve this problem, let's understand the logarithmic properties involved.
Consider the logarithm of a number [tex]\( a \)[/tex] to the base [tex]\( a \)[/tex]. We represent the logarithm of [tex]\( a \)[/tex] with base [tex]\( a \)[/tex] as [tex]\( \log_a(a) \)[/tex].
By definition, the logarithm [tex]\( \log_a(a) \)[/tex] is the exponent to which the base [tex]\( a \)[/tex] must be raised to produce the number [tex]\( a \)[/tex]. In other words, if we set [tex]\( \log_a(a) = x \)[/tex], then by the definition of logarithms:
[tex]\[ a^x = a \][/tex]
Here, [tex]\( x \)[/tex] is the exponent required to get back to the number [tex]\( a \)[/tex]. It is evident that the exponent [tex]\( x \)[/tex] must be 1 because raising [tex]\( a \)[/tex] to the power of 1 simply gives [tex]\( a \)[/tex]:
[tex]\[ a^1 = a \][/tex]
Therefore,
[tex]\[ \log_a(a) = 1 \][/tex]
So, the logarithm of any number to itself as base is:
(a) 1
