Correct Answer - Option 2 :
\(\frac{m + 3n}{2}\)
Calculation:
∵ logx162 = m
⇒ logx(34 × 2) = m
⇒ m = 4logx3 + logx2 ---(1)
∵ logx72 = n
⇒ logx(32 × 23) = n
⇒ n = 2logx3 + 3logx2 ---(2)
Solving (1) and (2) we get,
logx3 = (3m - n)/10
and logx2 = (2n - m)/5
Now logx7776 = logx(35 × 25)
= 5(logx3 + logx2)
= 5((3m - n)/10 + (2n - m)/5)
= 5((m + 3n)/10)
= (m + 3n)/2
In this type of question always try to factorize value inside the log and then use these formulas:
log(p × q) = log(p) + log(q)
log(p/q) = log(p) - log(q)