Is `log_5 3` equal to `log_3 5` ?

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justaguide | College Teacher | (Level 2) Distinguished Educator

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It has to be evaluated if `log_3 5 = log_5 3` .

Use the relation `log_a b = (log_x b)/(log_x a)`

Expressing `log_3 5` and `log_5 3` as an expression with a logarithm that has the same base:

`log_3 5 = (log_10 5)/(log_10 3)` ...(1)

`log_5 3 = (log_10 3)/(log_10 5)` ...(2)

From (1) and (2) it is seen that `log_3 5 != log_5 3` but rather `log_3 5 = 1/(log_5 3)`

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