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Math Help - log 5

  1. #1
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    log 5

    1. what is the logarithmic equation with the following transformations

    shifted 4 units left
    shifted 3 units up
    vertically compressed by 1/3
    horizontal stretch by 3

    2. write log_{2} (\frac{1}{4})=-2 in exponential form

    3. write 81^{\frac{3}{4}}=27 in logarithmic form

    4. what is x in the equation log_{\frac{1}{4}}x=-2
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  2. #2
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    Quote Originally Posted by william View Post
    1. what is the logarithmic equation with the following transformations

    shifted 4 units left
    shifted 3 units up
    vertically compressed by 1/3
    horizontal stretch by 3
    1) We've gone over transformations before, william.
    Shifting to the left means that f(x) changes to f(x + c).
    Shifting upwards means that f(x) changes to f(x) + c.
    A vertical shrink means that f(x) changes to c*f(x), where c is in 0 < c < 1.
    A horizontal stretch means that f(x) changes to f(x/c), where c > 1.

    Apply these transformations, one after another, to f(x) = log(x).

    2. write log_{2} (\frac{1}{4})=-2 in exponential form
    3. write 81^{\frac{3}{4}}=27 in logarithmic form
    If you have a logarithmic equation
    \log_b x = y,
    then the corresponding exponential form is
    b^y = x.

    4. what is x in the equation log_{\frac{1}{4}}x=-2
    Change the equation into exponential form.


    01
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  3. #3
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    Quote Originally Posted by yeongil View Post
    1) We've gone over transformations before, william.
    Shifting to the left means that f(x) changes to f(x + c).
    Shifting upwards means that f(x) changes to f(x) + c.
    A vertical shrink means that f(x) changes to c*f(x), where c is in 0 < c < 1.
    A horizontal stretch means that f(x) changes to f(x/c), where c > 1.

    Apply these transformations, one after another, to f(x) = log(x).



    If you have a logarithmic equation
    \log_b x = y,
    then the corresponding exponential form is
    b^y = x.


    Change the equation into exponential form.


    01
    thanks,for the equation i get f(x)= log(x+4)+3, i can't get the rest
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  4. #4
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    Quote Originally Posted by yeongil View Post
    1) We've gone over transformations before, william.
    Shifting to the left means that f(x) changes to f(x + c).
    Shifting upwards means that f(x) changes to f(x) + c.
    A vertical shrink means that f(x) changes to c*f(x), where c is in 0 < c < 1.
    A horizontal stretch means that f(x) changes to f(x/c), where c > 1.

    Apply these transformations, one after another, to f(x) = log(x).



    If you have a logarithmic equation
    \log_b x = y,
    then the corresponding exponential form is
    b^y = x.


    Change the equation into exponential form.


    01
    for 2 i get 2^-2=1/4<br />

    for 3 i get log_{3/4}27=81

    for 4 i get x=1/16<br />


    3
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