Which one is true for the mathematical expression (log√27+ log 8 - log√1000)/log 1.2

Question: Which one is true for the mathematical expression (log√27 + log 8 - log√1000)/log 1.2

Solution:
লব = log√27 + log 8 - log√1000
= log(3³)^1/2 + log 2³ - log(10³)^1/2
= 3/2 log 3 + 3 log 2 - 3/2 log 10
= 3/2 [log 3 + 2 log 2 - log 10]
= 3/2 [log 3 + log 4 - log 10]
= 3/2 [log {(3 × 4)/10}]
= 3/2 log (1.2)

প্রদত্ত রাশি = 3/2 × log 1.2/log 1.2
= 3/2