`log_27(9)` Evaluate the logarithm.

`log_27 (9)`

To evaluate, factor the 9.

`= log_27 (3^2)`

Then, apply the formula of change base `log_b (a) =(log_c(a))/(log_c(b))` .

`= (log_3(3^2))/(log_3 (27))`

`=(log_3 (3^2))/(log_3 (3^3))`

To simplify it further, apply the rule `log_b(a^m)= m*log_b(a)` .

`= (2* log_3(3))/(3*log_3(3))`

When the base and argument of the logarithm are the same, the result is 1, `log_b(b)=1` .

`= (2*3)/(3*1)`

`=2/3`

Therefore, `log_27 (9) =2/3` .

Comments

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