the difference between these two logarithmI was just wondering what is the difference between 1 ln ⁡ ( n 2 ) and 1 ln 2 ⁡ ( n ) I know that 1 ln ⁡ ( n 2 ) is 1 2 ln ⁡ ( n ) through the power rule, but I am not so sure about 1 ln 2 ⁡ ( n ) .

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the difference between these two logarithmI was just wondering what is the difference between             1              ln        ⁡        (                  n          2                )             and             1                        ln          2                ⁡        (        n        )            I know that             1              ln        ⁡        (                  n          2                )             is             1              2        ln        ⁡        (        n        )             through the power rule, but I am not so sure about             1                        ln          2                ⁡        (        n        )            .

Dahlia Pace · Accepted Answer

Not a good example:  n  =            e        2      ⟹        1          log      ⁡              n        2              =      1    4          1                  log        2            ⁡      n        =      1    4  Good example:  n  =            e        3      ⟹        1          log      ⁡              n        2              =      1    6          1                  log        2            ⁡      n        =      1    9

nonhumanWd3 · Accepted Answer

Let&#039;s say   x  =      1          ln      ⁡      n      , then      1          ln      ⁡              n        2              =      1          2      ln      ⁡      n        =      x    2        1                  ln        2            ⁡      n        =  (      1          ln      ⁡      n            )    2    =      x    2  You can clearly notice the difference between       x    2   and       x    2  . Hope it cleared your doubt.

The difference between these two logarithm I was just wondering what is the difference between 1/ln(n^2) and 1/ln^2(n)

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