Jika log p=a, log q=b, dan log r=c, nyatakan tiap bentuk

a) (1/2)a + b + 4c, b) (1/2)a - (1/3)b - 3c

Pembahasan

Diketahui log p = a, log q = b, dan log r = c.

a) log (akar(p) qr^4)
Menggunakan sifat-sifat logaritma:
log (akar(p) qr^4) = log (p^(1/2) q^1 r^4)
= log(p^(1/2)) + log(q^1) + log(r^4)
= (1/2) log p + 1 log q + 4 log r
= (1/2)a + b + 4c

b) log((akar(p))/(q^(1/3) r^3))
Menggunakan sifat-sifat logaritma:
log((akar(p))/(q^(1/3) r^3)) = log(p^(1/2)) - log(q^(1/3) r^3)
= log(p^(1/2)) - (log(q^(1/3)) + log(r^3))
= (1/2) log p - ((1/3) log q + 3 log r)
= (1/2)a - (1/3)b - 3c