To find the value of [tex]\(\log_3 3\)[/tex], let's break it down step by step.
1. Understanding Logarithms:
- The logarithm [tex]\(\log_b a\)[/tex] asks the question, "To what power must the base [tex]\(b\)[/tex] be raised, to get the number [tex]\(a\)[/tex]?"
2. Setting Up the Problem:
- We are given [tex]\(\log_3 3\)[/tex] and need to find its value.
- In mathematical terms, we are looking for [tex]\(x\)[/tex] in the equation [tex]\(3^x = 3\)[/tex].
3. Solving the Equation:
- Because the bases are the same, we can equate the exponents directly.
- Therefore, if [tex]\(3^x = 3^1\)[/tex], it implies that [tex]\(x = 1\)[/tex].
4. Conclusion:
- The value of [tex]\(\log_3 3\)[/tex] is [tex]\(1\)[/tex].
Thus, [tex]\(\log_3 3 = 1\)[/tex]. This matches the answer given.
