Jika alogp=x, alogq=y, dan alogr=z, nyatakan

a. 2x + 5y + 3z, b. 3x - 2y - 4z

Pembahasan

Diberikan alog(p) = x, alog(q) = y, dan alog(r) = z. Kita akan menyatakan logaritma berikut dalam x, y, dan z: a. alog(p^2 q^5 r^3) Menggunakan sifat logaritma log(a*b) = log(a) + log(b) dan log(a^n) = n*log(a): alog(p^2 q^5 r^3) = alog(p^2) + alog(q^5) + alog(r^3) = 2*alog(p) + 5*alog(q) + 3*alog(r) = 2x + 5y + 3z. b. alog((p^3)/(q^2 r^4)) Menggunakan sifat logaritma log(a/b) = log(a) - log(b): alog((p^3)/(q^2 r^4)) = alog(p^3) - alog(q^2 r^4) = alog(p^3) - (alog(q^2) + alog(r^4)) = 3*alog(p) - (2*alog(q) + 4*alog(r)) = 3x - (2y + 4z) = 3x - 2y - 4z.