Answer:
4Log₅ x + 5Log₅ y – Log₅ 2
Step-by-step explanation:
Log₅ (x⁴y⁵/2)
The above expression can be simplified as follow:
Log₅ (x⁴y⁵/2)
Recall:
Log(M/N) = Log M – Log N
Therefore,
Log₅ (x⁴y⁵/2) = Log₅ x⁴y⁵ – Log₅ 2
Recall
Log MN = Log M + Log N
Therefore,
Log₅ x⁴y⁵ – Log₅ 2
= Log₅ x⁴ + Log₅ y⁵ – Log₅ 2
Recall
Log Mⁿ = nLog M
Therefore,
Log₅ x⁴ + Log₅ y⁵ – Log₅ 2
= 4Log₅ x + 5Log₅ y – Log₅ 2
Thus,
Log₅ (x⁴y⁵/2)
= 4Log₅ x + 5Log₅ y – Log₅ 2
