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Log(base a)(a^4*b)-Log(base a)(a*b) is the same as

I got the answer as d since subtracting logs with the same base is division. However, the answer key saids its b, Can someone please help me with this?

  • Math -

    log(base a)(a^4*b)-log(base a)(a*b)
    = log(base a)[a^4b/ab]
    = log(base a) (a^3)

    The power to which a has to be raised to get a^3 is 3.

    That is what log(base a) a^3 means.

    The answer is 3.

  • Math -

    Ooo right, my teacher mentioned that, guessed it slipped my mind. Thanks a lot. Diploma tomorrow :(

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