3log4 = p dan 5log3 = q, nilai log 45

jawab

³log 4 = p
⁵log 3 = q
⁵log 3 . ³log 4 = pq
⁵log 4 =pq
⁵log 2²  = pq
2 ⁵log 2 = pq
⁵log 2 = 1/2 pq

log 45 = ⁵log 45 /⁵log 10
log 45 = (⁵log 3² + ⁵log 5) / (⁵log 5 + ⁵log 2)
= ( 2.⁵log 3 + 1)  / (1 + 1/ p)
= ( 2 q + 1)/(1 +  1/p) ....}kalikan p/p
= (2 pq + p )/ (p+1)

LogAritMa

³log 4 = p ---> ³log 2 = p/2
5'log 3 = q

log 45
= ³log 45 / ³log 10
= ³log (3² × 5) / ³log (2 × 5)
= (2 . ³log 3 + ³log 5) / (³log 2 + ³log 5)
= (2 + 1/q) / (p/2 + 1/q)
= ((2q + 1)/q) / ((pq + 2)/2q)
= 2(2q + 1) / (pq + 2)
= (4q +2) / (pq + 2)