jika ab^log a = 1/3 dan a^log bc = 3/2 maka nilai c^log a adalah

Bab Logaritma
Matematika SMA Kelas X

(ab)^log a = 1/3
1/(a^log (ab)) = 1/3
a^log (ab) = 3
ab = a^3
b = a²

a^log bc = 3/2
a^log (a²c) = 3/2
a^log a² + a^log c = 3/2
2 + a^log c = 3/2
a^log c = 3/2 - 2
a^log c = -1/2
1/(c^log a) = 1/-2
c^log a = -2

Diketahui :
ab^log a = 1/3
a^log bc = 3/2

Ditanya : c^log a ?

Dijawab
ab^log a = 1/3
1 / (a^log ab) = 1/3
a^log ab = 3
a^log ab = a^log a³
ab = a³
b = a³ / a
b = a²

a^log bc = 3/2
a^log (a².c) = 3/2
a^log a² + a^log c = 3/2
2 . a^log a + a^log c = 3/2
2 + a^log c = 3/2
a^log c = 3/2 - 2
a^log c = 3/2 - 4/2
a^log c = -1/2
1 / (c^log a) = -1/2
c^log a = 2 / (-1)
c^log a = -2

Jadi, nilai dari c^log a adalah -2