Let f(x) = log(x). Find values of a such that f(kaa) = kf(a).

Answer:a = [tex]k^{\frac{1}{k-2}}[/tex] Step-by-step explanation:Given:f(x) = log(x)and,f(kaa) = kf(a)now applying the given function, we get⇒ log(kaa) = k × log(a)or⇒ log(ka²) = k × log(a)Now, we know the property of the log function thatlog(AB) = log(A) + log(B)and,log(Aᵇ) = b × log(A)Thus,⇒ log(k) + log(a²) = k × log(a)         (using log(AB) = log(A) + log(B) )or⇒ log(k) + 2log(a) = k × log(a)            (using log(Aᵇ) = b × log(A) )or⇒ k × log(a) - 2log(a) = log(k)or⇒ log(a) × (k - 2) = log(k)or⇒ log(a) = (k - 2)⁻¹ × log(k)or⇒ log(a) = [tex]\log(k^{\frac{1}{k-2}})[/tex]          (using log(Aᵇ) = b × log(A) )taking anti-log both sides⇒ a = [tex]k^{\frac{1}{k-2}}[/tex]