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:a = 2 Step-by-step explanation:givenf(x) = log(x)                                              .....1and f(2a) = 2f(a)now,since f(x) = log(x)                then f(2a) = log(2a)        put x=2a           ......2and  f(a) =  log(a)            put x=a             ......3 now from eq 1 and eq 2 and eq 3log(2a) =2 log (a)log(2) + log(a) =2 log (a)                note; Log property log (m x n)= log m+log nlog(2) = 2log(a)-log(a)log(2) = log(a)or a= 2