Answer:
a = 1.7318
Step-by-step explanation:
Given function in the question f(x) = log(x)
also,
f(3a) = 3f(a)
To find: the value of 'a'
now,
f(3a) = 3f(a)
⇒ log(3a) = 3 × log(a)
now,
we know the property of the log function that
log(AB) = log(A) + log(B)
therefore,
⇒ log(3) + log(a) = 3 × log(a)
or
⇒ log(3) = 3 × log(a) - log(a)
or
⇒ 2log(a) = log(3)
now,
log(3) = 0.4771
thus,
⇒ 2log(a) = 0.4771
or
log(a) = 0.2385
taking anti-log both sides, we get
a = [tex]10^{0.2385}[/tex]
or
a = 1.7318
