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.

a = 2

Step-by-step 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