Answer:
½Log 57 – ½Log 74
Explanation:
Logb √(57/74)
We can expand the above expression as follow:
Logb √(57/74)
Logb √57 /√74
Recall:
logM/N = Log M – Log N
Therefore,
Logb √57/√74 = Logb √57 – Logb √74
Recall:
Log √M = Log M^1/2
Therefore,
Logb √57 = Logb 57^1/2
Logb √74 = Logb 74^1/2
Logb √57 – Logb √74 = Logb 57^1/2 – Logb 74^1/2
Recall:
Log M^1/2 = ½Log M
Therefore,
Logb 57^1/2 = ½Log 57
Logb 74^1/2 = ½Log 74
Logb 57^1/2 – Logb 74^1/2 = ½Log 57 – ½Log 74
From the illustrations above, we see that:
Logb √(57/74) = ½Log 57 – ½Log 74