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Math Help - Logarithmic Functions

  1. #1
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    Logarithmic Functions

    Could someone please solve these questions for me? Thanks
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    Re: Logarithmic Functions

    Quote Originally Posted by strangepath View Post
    Could someone please solve these questions for me? Thanks
    First, we are not a homework service. Please post what work you've been able to do on these.

    Second. Please only post, say, three problems in any single thread. It just gets too messy for the members to help you.

    -Dan
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  3. #3
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    Re: Logarithmic Functions

    Hello, strangepath!

    That's quite a list, but I see that they require a variety of tecnniques.
    I'll solve a few of them.


    \text{(1) Solve for }n\!:\;\;11^{n+1} \:=\:13

    Take logs: . \ln(11^{n+1}) \:=\:\ln(13) \quad\Rightarrow\quad(n+1)\ln(11) \:=\:\ln(13)

    . . . . . . . . . n+1 \:=\:\frac{\ln(13)}{\ln(11)} \quad\Rightarrow\quad n \:=\:\frac{\ln(13)}{\ln(11)} - 1




    \text{(4) Solve for }x\!:\;\;5^{x+1} - 5^x \:=\:8

    This one is deceptively simple.

    Factor: . 5^x(5-1) \:=\:8 \quad\Rightarrow\quad 5^x\cdot4 \:=\:8 \quad\Rightarrow\quad 5^x \:=\:2

    Take logs: . \ln(5^x) \:=\:\ln(2) \quad\Rightarrow\quad x\ln(5) \:=\:\ln(2) \quad\Rightarrow\quad x \:=\:\frac{\ln(2)}{\ln(5)}




    \text{(7) Solve for }x\!:\;\;10^{4\log x} \:=\:16

    We are expected to know that: . 10^{4\log x} \:=\:10^{\log x^4} \:=\:x^4

    The equation becomes: . x^4 \:=\:16 \quad\Rightarrow\quad x \:=\:2

    . . . We must discard x = -2.



    \text{(8) Solve for }w\!:\;\;3e^w - 35e^{-w} \:=\:-16

    Multiply by e^w\!:\;\;3e^{2w} - 35 \:=\:-16e^w \quad\Rightarrow\quad 3e^{2w} + 16e^w - 35 \:=\:0

    Factor: . (e^w + 7)(3e^w - 5) \:=\:0


    And we have two equations to solve:

    . . \begin{Bmatrix}e^w + 7 \:=\:0 & \Rightarrow & e^w \:=\:\text{-}7 &\Rightarrow & \text{no real roots} \\ \\ 3e^w - 5 \:=\:0 & \Rightarrow& e^w \:=\:\frac{5}{3} & \Rightarrow & w \:=\:\ln(\frac{5}{3}) \end{Bmatrix}
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    Re: Logarithmic Functions

    Quote Originally Posted by topsquark View Post
    First, we are not a homework service. Please post what work you've been able to do on these.

    Second. Please only post, say, three problems in any single thread. It just gets too messy for the members to help you.

    -Dan
    Sorry about that.
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  5. #5
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    Re: Logarithmic Functions

    To Soroban

    Thanks for the help. I think I will be able to manage with the rest.
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