To determine the base of the logarithm for which [tex]\( 36^2 \)[/tex] is the result, we need to work through the problem step by step:
1. Calculate the power: [tex]\( 36^2 \)[/tex].
[tex]\[ 36^2 = 1296 \][/tex]
2. Consider the given base options: [tex]\( 2, 1296, 6, 36 \)[/tex].
3. Identify the base that correctly satisfies [tex]\( \text{base}^2 = 1296 \)[/tex].
- For base 2: [tex]\( 2^2 = 4 \)[/tex]. This does not match 1296.
- For base 1296: [tex]\( 1296^2 = 1679616 \)[/tex]. This exceeds 1296.
- For base 6: [tex]\( 6^2 = 36 \)[/tex]. This does not match 1296.
- For base 36: [tex]\( 36^2 = 1296 \)[/tex]. This is the desired result.
Hence, the base of the logarithm that satisfies [tex]\( 36^2 = 1296 \)[/tex] is:
[tex]\[ \boxed{36} \][/tex]
