D1 = log2 = m log3 = n D2 = A) log24 B) ¹²log54

D1= log2 =m
log 3=n
D2=A)log24
B)¹²log54
D1=log2=m log3=n D2=A)log24 B)¹²log54

log 2 = m, log 3 = n
a) log 24
= log (8 x 3)
= log 8 + log 3
= log 2^3 +' log 3
= 3.log 2 + log 3
= 3 m + n
b) 12log 54
= log 54 / log 12
= log (27 x 2) / log (4 x 3)
= ( log 27 + log 2 ) / (log 4 + log 3)
= ( log 3^3 + log 2) /( log 2^2 + log 3)
= (3.log 3 + log 2) / (2.log2 + log 3)
= (3n + m) / (2m + n)
= ( m + 3n ) / (2m + n)