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Changing the Base

By definition, $ x = b^{\log_b(x)}$. Taking the log base $ a$ of both sides gives

$\displaystyle \log_a(x) = \log_b(x) \log_a(b)

which tells how to convert the base from $ b$ to $ a$, that is, how to convert the log base $ b$ of $ x$ to the log base $ a$ of $ x$. (Just multiply by the log base $ a$ of $ b$.)

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