Algebra-Mathmate or Reiny or Dr. Bob, please check

I have two short questions which I think I know the answer-could you please check?

If I write log(b)x - 2log(b)y as a single logarithm it would be log(b) x/y^2, correct? If not please help

and Is the function f(x) = 1/x a exponential function -I think it would be because it could be a number to the negative power, correct or would that be false

The function f(x) = logx is a logarthmic function-I think this is false because it should be written as log(then a number)x, correct

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asked by Anna
  1. Could one of you please check when you have time.

    Thank you

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    posted by Anna
  2. correct, if you meant logb(x/y^2)

    F(x)=x^-1 is an inverse function, not an exponential function. Exponential functions are functions which can be written as f(x)=k e^ax

    for instance f(x)=3e^-5

    or f(x)=12(1-e^(-4x) )

    Can it be applied to g(x)=3 a^bx ?

    many people include this form in the definition of exponential functions.

    I would call f(x)=log x a log function, it is a log whether or not the base is defined. changing bases just changes the slopes of the log curves.

  3. Thank you for the explanations- I appreciate it

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    posted by Anna
  4. I just noticed something-I had asked about if f(x) = 1/x is an exponential function and I think you rewrote it as f(x) = x^-1. Therefore, f(x) = 1/x is NOT an exponential function, correct?

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    posted by Anna
  5. correct, not an exponential function.

  6. Thank you-could you look at my new post-I just needed clarification about f(x) = logx you said this would be true but doesn't it need parentheses or a separation between log and x for this to be correct?

    Thank you

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    posted by Anna

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