loga x = 1, loga y = 2 হলে, loga z = 3 হলে, loga \((\frac{{{x^{3\;}}\;{y^{2\;}}\;}}{z})\) এর মান কত ?

log_a x = 1, log_a y = 2 হলে, log_a z = 3 হলে, log_a \((\frac{{{x^{3\;}}\;{y^{2\;}}\;}}{z})\) এর মান কত ?

A 1

B 2

C 4

D 5

Correct Answer: Option C

log_a x = n x = aⁿ

log_a x = 1 a¹ = x x = a¹ = a

log_a y = 2 a² = y y = a²

log_a z = 3 a³ = z z = a³

log_a \((\frac{{{x^{3\;}}\;{y^{2\;}}\;}}{z})\) = log_a \((\frac{{{x^{3\;}}\;{y^{2\;}}\;}}{z})\) = log_a a⁴ = 4 log_a a = 4 \( \times \)1 = 4