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When you see (log a)², it means "the square of the logarithm of a." In other words, it's (log a) * (log a), which is the square of the logarithm of the number a.
On the other hand, log² a means "the logarithm of a squared." It's equivalent to log(a * a), which is the logarithm of the number a squared.
So, they represent different operations, and in general, they are not equal
- When you see "log^n" with a base of 10, it typically means taking the logarithm of a value multiple times.
For example:
- log^2 a would mean taking the logarithm of a, and then taking the logarithm of the result again.
- log^3 a would mean taking the logarithm of a, then taking the logarithm of the result, and then taking the logarithm of that result again.
It's essentially repeated logarithmic operations with a base of 10.
