Question

I don’t understand this stuff

Answer 1

Answer:

½Log 57 – ½Log 74

Step-by-step 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