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Answer :
To solve this question, we want to express the equation [tex]\(13^2 = 169\)[/tex] in logarithmic form. Here's a step-by-step explanation of how we do that:
1. Understand Exponentiation: The expression [tex]\(13^2 = 169\)[/tex] means that 13, when raised to the power of 2, results in 169.
2. Logarithmic Form: In general, logarithmic form is another way to represent exponentiation. The logarithmic form of [tex]\(b^e = a\)[/tex] is [tex]\(\log_b(a) = e\)[/tex], where:
- [tex]\(b\)[/tex] is the base,
- [tex]\(a\)[/tex] is the result,
- [tex]\(e\)[/tex] is the exponent.
3. Identify Components: In the given expression [tex]\(13^2 = 169\)[/tex]:
- The base [tex]\(b\)[/tex] is 13,
- The result [tex]\(a\)[/tex] is 169,
- The exponent [tex]\(e\)[/tex] is 2.
4. Convert to Logarithmic Form: Using the components identified, we convert [tex]\(13^2 = 169\)[/tex] to:
[tex]\[
\log_{13}(169) = 2
\][/tex]
Therefore, the logarithmic form of [tex]\(13^2 = 169\)[/tex] is [tex]\(\log_{13}(169) = 2\)[/tex]. This matches the first option given in the multiple choice list.
1. Understand Exponentiation: The expression [tex]\(13^2 = 169\)[/tex] means that 13, when raised to the power of 2, results in 169.
2. Logarithmic Form: In general, logarithmic form is another way to represent exponentiation. The logarithmic form of [tex]\(b^e = a\)[/tex] is [tex]\(\log_b(a) = e\)[/tex], where:
- [tex]\(b\)[/tex] is the base,
- [tex]\(a\)[/tex] is the result,
- [tex]\(e\)[/tex] is the exponent.
3. Identify Components: In the given expression [tex]\(13^2 = 169\)[/tex]:
- The base [tex]\(b\)[/tex] is 13,
- The result [tex]\(a\)[/tex] is 169,
- The exponent [tex]\(e\)[/tex] is 2.
4. Convert to Logarithmic Form: Using the components identified, we convert [tex]\(13^2 = 169\)[/tex] to:
[tex]\[
\log_{13}(169) = 2
\][/tex]
Therefore, the logarithmic form of [tex]\(13^2 = 169\)[/tex] is [tex]\(\log_{13}(169) = 2\)[/tex]. This matches the first option given in the multiple choice list.
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