We know when three terms say a,b,c are in GP

We can write

b² = a.c

∴ According to the given data

We can write

(a^x/2)² = log_xa . log_bx

a^x = log_xa . log_bx

⇒

⇒ a^x = log_ba

Multiplying by log_a to both sides we get

⇒ log_a (a^x) = log_a (log_ba)

⇒ x log_aa = log_a (log_ba)

⇒ x = log_a (log_ba)