Is log ⁡ ( n ) = 1 2 ∗ ( log ⁡ n )?

Question

Is       log    ⁡    (    n    )    =      1          2        ∗  (  log  ⁡  n  )?

hayaniqWf · Accepted Answer

You are mixing up several identities. The following are true:

\log (\sqrt{n}) = \log (n^{\frac{1}{2}}) = \frac{1}{2} \log (n)

\log (n^{\frac{1}{\sqrt{2}}}) = \frac{1}{\sqrt{2}} \log (n)

Emilia Carpenter · Accepted Answer

No.Let&#039;s interpret   log as the decadic logarithm (base = 10), and let   n  =  10000      log    ⁡    (    n    )    =      log    ⁡    (    10000    )    =      4    =  2On the other side:      1          2        ∗  (  log  ⁡  n  )  =      1          2        ∗  (  log  ⁡  10000  )  =      1          2        ∗  4  =  2  ∗      2  Since   2  ≠  2  ∗      2  , both terms are not equal.If you prefer to interpret   log as natural logarithm, then let   n  =      e    4  , and you get the same results.

Is sqrt(log (n))=1/( sqrt(2))*(log n)?

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