To solve the given question, we need to find the value of the logarithm expression [tex]\(\log_a 2\)[/tex].
The expression [tex]\(\log_a 2\)[/tex] represents the logarithm of 2 with base [tex]\(a\)[/tex]. It essentially asks for the exponent to which [tex]\(a\)[/tex] must be raised to get 2. However, without knowing the value of [tex]\(a\)[/tex], we cannot determine a specific numerical value for [tex]\(\log_a 2\)[/tex] because the value of the logarithm depends on both the number and the base.
Given the options:
(a) 0
(b) 1
(c) a
(d) 10
We can analyze each:
- If [tex]\(\log_a 2 = 0\)[/tex], it would imply [tex]\(a^0 = 2\)[/tex], but [tex]\(a^0 = 1\)[/tex] for any non-zero [tex]\(a\)[/tex], so this is not possible.
- If [tex]\(\log_a 2 = 1\)[/tex], it would imply [tex]\(a^1 = 2\)[/tex], which means [tex]\(a = 2\)[/tex]. But we do not have sufficient information to confirm [tex]\(a = 2\)[/tex] for every scenario.
- If [tex]\(\log_a 2 = a\)[/tex], it would imply [tex]\(a^a = 2\)[/tex] which is not generally true without a specific value of [tex]\(a\)[/tex].
- If [tex]\(\log_a 2 = 10\)[/tex], it would imply [tex]\(a^{10} = 2\)[/tex], which again cannot be generally true without knowing [tex]\(a\)[/tex].
Without any information about [tex]\(a\)[/tex], we cannot definitively determine any specific value from the given options. Hence, the correct approach is to acknowledge that it is not possible to determine the value of [tex]\(\log_a 2\)[/tex] with the given information and options.
Thus, the conclusion is:
None of the given options (0, 1, a, 10) are determinable as the value of [tex]\(\log_a 2\)[/tex] without additional information.
