Jawab:
(a.) ²¹log 48 = (4+a) ÷ (ab+a)
(b.) ⁴²log 56​ = (3+ab) ÷ (1+a+ab)

Penjelasan:
Diketahui:
²log3 = a, ³log7 = b
ln3÷ln2 = a,  ln7÷ln3 = b
ln3 = aln2,    ln3 = ln7÷b
ln2 = ln3÷a   ln7 = b ln3

(a.) ²¹log 48 = ln48 ÷ ln21
= ln(8·6) ÷ ln(7·3)
= ln(2³·2·3) ÷ (ln7 + ln3)
= ln(2⁴·3) ÷ (ln7 + ln3)
= (ln2⁴ + ln3) ÷ (ln7 + ln3)
= (4ln2 + ln3) ÷ (ln7 + ln3)
= ((4ln3÷a) + ln3) ÷ (b ln3 + ln3)
= (ln3((4÷a) + 1)) ÷ (ln3(b+1))
= ((4÷a) + 1) ÷ (b+1)
= ((4÷a) + (a÷a)) ÷ (b+1)
= ((4+a)÷a) ÷ (b+1)
= (4+a) ÷ (a(b+1))
= (4+a) ÷ (ab+a)

(b.) ⁴²log 56​ = ln56 ÷ ln42
= ln(8·7) ÷ ln(6·7)
= ln(2³·7) ÷ ln(2·3·7)
= (ln(2³) + ln7) ÷ (ln2 + ln3 + ln7)
= (3ln2 + ln7) ÷ (ln2 + ln3 + ln7)
= ((3ln3÷a) + b ln3) ÷ ((ln3÷a) + ln3 + b ln3)
= (ln3((3÷a)+b)) ÷ (ln3((1÷a)+1+b))
= ((3÷a)+b) ÷ ((1÷a)+1+b)
= ((3÷a)+(ab÷a)) ÷ ((1÷a)+(a÷a)+(ab÷a))
= ((3+ab)÷a) ÷ ((1+a+ab)÷a)
= (3+ab) ÷ (1+a+ab)

(xcvi)