I can't understand if there is any such formula for $(\log_{b}a)^2$. Are there any? $\log_{b}(a^2) = 2\log_{b}{a}$
But if the whole log is squared is there any such formula or the same formula is used?
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No there is no such formula for the square of a log. You need to leave $\log_b(a)^2$ as a the final answer. – Cyclone May 13 '16 at 16:31
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@Ritwika Try to phrase the question as best as possible, that way people can understand what you are saying. – Arbuja May 13 '16 at 16:38
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Note that $\left(\log_{b}a\right)^{2}=\left(\log_{b}a\right)\left(\log_{b}a\right)$
There is a general formula for multiplying exponents just like there is a general formula for adding logs.
However, there is no general log formula for multiplying logs just like there is no general formula for adding exponents.
Arbuja
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We can't really simplify the expression $(\log_b a)^2$ since there exist no useful identities for powers of logarithms. Recall that, in some sense, logarithms themselves are powers.
If you're really insistent on eliminating the square, there are several ways to rewrite the expression, such as $$(\log_b a)^2=\log_b(a^{\log_b a})=\dfrac{\log_b a}{\log_a b},$$ albeit these are computationally no better.
Corellian
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