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23 April, 19:20

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.

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  1. 23 April, 20:09
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    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
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