Question

Let f(x) = log(x). Find values of a such that f(3a) = 3f(a).

Answer 1

a = 1.7318

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 =
`10^(0.2385)`

or

a = 1.7318