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Math Help - exponential inverse problem

  1. #1
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    exponential inverse problem

    exponential inverse problem-photo-1-.jpg
    need the answer to this question asap.
    thanks in advance.
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  2. #2
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    Re: exponential inverse problem

    Hello, rainxspear!

    Do you know the procedure for finding an inverse function?


    If f(x) \:=\:\log_4(x+5)+3,
    what is the function g(x) if f(x) and g(x) are inverses?

    \text{We have: }\:y \;=\;\log_4(x+5)+3

    \text{Interchange }x\text{ and }y\!: \;x \:=\:\log_4(y+5) + 3

    \text{Solve for }y\!:\;x - 3 \;=\;\log_4(y+5)

    = . . . . . . . . 4^{x-3} \;=\;y+5

    . . . . . . . 4^{x-3} - 5 \;=\;y


    Therefore: . g(x) \;=\;4^{x-3} - 5
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  3. #3
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    Re: exponential inverse problem

    Thank you so much, that cleared up things so immensely.
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  4. #4
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    Re: exponential inverse problem

    You do realize that this is a help site, not an answer site. To help you so that you can answer questions on your own during your test, we must see what you are doing on your practice problems. Please show your work in the future.

    One way to solve these inverse problems is: (1) state f(x) = y, (2) solve for x in terms of y, (3) switch x and y, and (4) replace y with g(x), you are done.

    So y = what?

    So x = what?

    What do you get when you switch x and y?

    I'll get you started.

    $f(x) = log_4(x + 5) - 3.$

    $y = log_4(x + 5) - 3 \implies y + 3 = log_4(x + 5) \implies x + 5 = 4^{y - 3} \implies what?$
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