`log_4(128)` Evaluate the logarithm. |

`log_4(128)`

To evaluate, factor 128.

`= log_4 (2^7)`

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

`= (log_2 (2^7))/(log_2 (4))`

`= (log_2 (2^7))/(log_2 (2^2))`

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

`= (7*log_2 (2))/(2*log_2(2))`

When the base and argument of logarithm are the same, it simplifies to 1, `log_b (b) = 1` .

`= (7*1)/(2*1)`

`=7/2`

Therefore, `log_4 (128) = 7/2` .

`log_4(128)`

To evaluate, factor 128.

`= log_4 (2^7)`

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

`= (log_2 (2^7))/(log_2 (4))`

`= (log_2 (2^7))/(log_2 (2^2))`

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

`= (7*log_2 (2))/(2*log_2(2))`

When the base and argument of logarithm are the same, it simplifies to 1, `log_b (b) = 1` .

`= (7*1)/(2*1)`

`=7/2`

Therefore, `log_4 (128) = 7/2` .