Question

Let f(x) = log(x). Find a value for a such that f(2a) = 2f(a). Is there one? Show work to justify your answer.

Answer 1

a = 2

Explanation:

given

f(x) = log(x) .....1

and f(2a) = 2f(a)

now,since f(x) = log(x)

then f(2a) = log(2a) put x=2a ......2

and f(a) = log(a) put x=a ......3

now from eq 1 and eq 2 and eq 3

log(2a) =2 log (a)

log(2) + log(a) =2 log (a) note; Log property log (m x n)= log m+log n

log(2) = 2log(a)-log(a)

log(2) = log(a)

or a= 2