`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` .
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